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Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert calculus; Grassmannian; Littlewood-Richardson rule; numerical homotopy continuation | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials affine Kac-Moody Lie algebra; integrable highest weight modules; root components; Virasoro algebra; higher cohomology vanishing; Schubert varieties; partial flag varieties | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials graph of monomial ideals; multigraded Hilbert scheme; Schubert scheme; Gröbner bases; Gröbner degenerations; Stanley-Reisner ideals DOI: 10.1016/j.jpaa.2004.12.030 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials holomorphic foliations; polar classes; Schubert cycles; Chern-Mather classes; invariant varieties Mol (R.S.).- Classes polaires associées aux distributions holomorphes de sous-espaces tangents. Bull. Braz. Math. Soc. (N.S.), 37(1):29-48, (2006). Zbl1120.32019 MR2223486 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials additive Strassen conjecture; symmetric tensors; computational complexity; polynomials \beginbarticle \bauthor\binitsE. \bsnmCarlini, \bauthor\binitsM. V. \bsnmCatalisano and \bauthor\binitsL. \bsnmChiantini, \batitleProgress on the symmetric Strassen conjecture, \bjtitleJ. Pure Appl. Algebra \bvolume219 (\byear2015), no. \bissue8, page 3149-\blpage3157. \endbarticle \OrigBibText Enrico Carlini, Maria Virginia Catalisano, and Luca Chiantini, Progress on the symmetric Strassen conjecture , J. Pure Appl. Algebra 219 (2015), no. 8, 3149-3157. \endOrigBibText \bptokstructpyb \endbibitem | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials cohomology; line bundles; Schubert varieties P. Polo, Variétés de Schubert et excellentes filtrations, Astérisque 173{174 (1989), no. 10-11, 281-311.} | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck groups; torsion subgroup of the Chow group | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials complex multiplication; singular moduli; resultant of the class polynomials; orders; fundamental discriminants of imaginary quadratics Hutchinson, T.: A conjectural extension of the Gross-Zagier formula on singular moduli. Tokyo J. Math. 21, 255--265 (1998) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials regular local ring; Azumaya algebra; Grothendieck conjecture for Hermitian spaces | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck-Riemann-Roch theorem; algebraic schemes; algebraic \({\mathbb{C}}\)-schemes [F-G]W. Fulton, H. Gillet: ``Riemann Roch for general Algebraic Varieties{'', Bull. Soc. Math. France 111 (1983) pp. 287--300.} | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Littlewood-Richardson coefficients; flag varieties; Schubert varieties; semisimple groups; Kac-Moody groups; reflection groups; Cartan matrices; Weyl groups Berenstein, A; Richmond, E, Littlewood-Richardson coefficients for reflection groups, Adv. Math., 284, 54-111, (2015) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Hurwitz numbers of polynomials; moduli space of curves; intersection numbers Shadrin, S.: Polynomial Hurwitz numbers and intersections on M\={}0,k. Funct. anal. Appl. 37, 78-80 (2003) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quartic double solid; intermediate Jacobian; Abel-Jacobi map; theta divisor A. S. Tikhomirov, New component of the moduli space \?(2;0,3) of stable vector bundles on the double space \?³ of index two, Acta Appl. Math. 75 (2003), no. 1-3, 271 -- 279. Monodromy and differential equations (Moscow, 2001). | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials rationally smooth Schubert varieties; Young's lattice Billey, S., and Mitchell, S., Affine partitions and affine Grassmannians, preprint 46pp: arXiv:0712.2871 (2007), to appear in the Electronic Journal of Combinatorics. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials locally nilpotent derivations; polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert variety; Littlewood-Richardson rule; puzzle; measure Bercovici, H.; Li, W. S.; Timotin, D.: A family of reductions for Schubert intersection problems, J. algebraic combin. 33, 609-649 (2011) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials decomposition of birational morphism; smooth curves on surfaces; with rational double points; blow-up of a smooth point; Gorenstein; threefold singularities D. Morrison, ''The biratioanl geometry of surfaces with ratiional double points,''Math. Ann.,271, 415--438 (1985). | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials non-commutative Chow motive; Grothendieck group; semi-simplicity M. Marcolli and G. Tabuada, Noncommutative motives, numerical equivalence, and semi-simplicity, Amer. J. Math. 136 (2014), no. 1, 59-75. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials characteristic classes; characteristic number; genus; singular space; motivic; additivity; Riemann-Roch; Grothendieck group; cobordism group; Hodge structure; mixed Hodge module Brasselet, J-P; Schürmann, J.; Yokura, S., Hirzebruch classes and motivic Chern classes for singular spaces, J. Topol. Anal., 2, 1-55, (2010) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials algebraic surface; bicanonical map; Du Val double plane; Burniat surface; bidouble cover C. Werner, On surfaces with pg= 0 and K2= 5, Canad. Math. Bull. 53 (2010), 746--756. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials polynomial functions on Lie algebra; compact connected Lie group; maximal torus; flag variety; cellular decomposition; Weyl group; Schubert cycles; equivariant cohomology; reduced decompositions A. Arabia, Cycles de Schubert et cohomologie équivariante de \?/\?, Invent. Math. 85 (1986), no. 1, 39 -- 52 (French). | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials toric variety; logarithmic double complex; de Rham complex; simplicial fan; hypercohomology groups; vanishing theorems; Ishida's cohomology groups T. Oda: ''The algebraic de Rham theorem for toric varieties'',Tohoku Math. J., Vol. 2, (1993), pp. 231--247. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials projective normality; vanishing cohomology groups; Schubert variety; line bundle; Frobenius morphism [RR]Ramanan, S. \&Ramanathan, A., Projective normality of flag varieties and Schubert varieties.Invent. Math., 79 (1985), 217--224. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials disconjugacy; Wronskian; Schubert calculus | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Gromov invariants; scheme of morphisms; special Schubert cycles; Chern classes; trivial bundles on Riemann surfaces; Quot schemes Bertram A.: Towards a Schubert calculus for maps from a Riemann surface to a Grassmannian. Internat. J. Math. 5, 811--825 (1994) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Cartan matrix; flag manifolds; Schubert calculus DOI: 10.1016/j.jsc.2004.03.005 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials positive definite form; sum of squares; Gram matrix; zero set of polynomials Gregory C. Verchota, Noncoercive sums of squares in \Bbb R[\?\(_{1}\),\ldots ,\?_{\?}], J. Pure Appl. Algebra 214 (2010), no. 3, 236 -- 250. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Laurent polynomials; Igusa's zeta function; explicit formulae; Newton polytopes; non-degeneracy conditions | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials noncommutative tori; Anasov automorphisms; C*-algebras; K-theory; cluster C*-algebras; Sklyanin algebras; AF-algebras; UHF-algebras; Hecke eigenform; continuous geometries; Connes geometries; index theory; Kasparov KK-theory; Jones polynomials; quantum groups; Hopf algebra; noncommutative algebraic geometry; deformation quantization | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials polynomials; divisors; partitions of integers; pseudo-geometric sequences | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials hyperelliptic locus of line bundle; double cover; polarized surfaces of \(\Delta\)-genus Aldo Biancofiore, Maria Lucia Fania, and Antonio Lanteri, Polarized surfaces with hyperelliptic sections, Pacific J. Math. 143 (1990), no. 1, 9 -- 24. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Robinson-Schensted insertion; Schubert calculus; Pieri formula; affine Grassmannian Lam, T., Lapointe, L., Morse, J., Shimozono, M.: Affine insertion and Pieri rules for the affine Grassmannian. Mem. Am. Math. Soc. \textbf{208}, 977 (2010) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials rings arising in quantum group theory; generic coordinate algebras; quantum Grassmannians; quantum minors; quantum Schubert varieties; normal domains T. H. Lenagan and L. Rigal, Quantum analogues of Schubert varieties in the Grassmannian, Glasg. Math. J. 50 (2008), no. 1, 55 -- 70. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Poincaré polynomials of degenerate flag varieties Feigin, E, The Median Genocchi numbers, \(q\)-analogues and continued fractions, Eur. J. Comb., 33, 1913-1918, (2012) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Riemann-Hilbert problem; Donaldson-Thomas theory; Barnes double gamma function | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Samaev's summation polynomials; Stange's elliptic nets; index calculus attack | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials algebraic curves; algebraic surfaces; forms; automorphisms; fibrations; coverings; vector fields; singularities; rational double points | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Borel subgroup; semi-simple group; Schubert filtration; Schubert varieties; antidominant weight; excellent filtration Polo, P, Modules associés aux variétés de Schubert, C. R. Acad. Sci. Paris Sér. I Math., 308, 123-126, (1989) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double covering of curves | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials differential modules; Levelt-Turrittin polynomials; nearby cycles | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert cycles R. Vakil, Schubert induction. Ann. Math. 164, 489--512 (2006) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials super Schubert cells; analytic supermanifold; Frobenius form; supergravity; Penrose transformation; complex supermanifold; sheaf of analytic Grassmann algebras; flag spaces; Berezinian | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials word maps; finite groups of Lie type; equidistribution; trace polynomials Bandman, T.; Kunyavskii, B., Criteria for equidistribution of solutions of word equations on \(S L(2)\), J. Algebra, 382, 282-302, (2013) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials \(D\)-module; \(F\)-crystal; \(p\)-curvature; adjoint operator; rings of differential operators; crystalline cohomology; niveau; Grothendieck-Hartshorne duality; Frobenius-action Berthelot, Pierre, \(\mathcal{D}\)-modules arithmétiques. II. Descente par Frobenius, Mém. Soc. Math. Fr. (N.S.), 81, vi+136 pp., (2000) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials hyperKähler manifold; orbifold; representation of fundamental group; E-polynomial; Hodge polynomial; Hitchin map; SYZ fibration; mirror partner; stringy mixed Hodge polynomials; mirror symmetry; Langlands duality Hausel, T.; Thaddeus, M.: Examples of mirror partners arising from integrable systems. C. R. Acad. sci. Paris sér. I math. 333, No. 4, 313-318 (2001) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials exterior differential system; integral k-flag; Schubert manifold | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Campedelli surfaces; involutions on surfaces; double covers Calabri, A., Mendes Lopes, M., Pardini, R.: Involutions on numerical Campedelli surfaces. Tohoku Math. J. 60(1), 1--22 (2008) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials surface singularity; double point; resolution of singularity; fundamental cycle; fiber cycle A. Calabri - R. Ferraro, Explicit resolutions of double point singularities of surfaces, Collect. Math. 53 (2002), 99--131. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Krichever-Novikov algebras; automorphism groups; Pell's equation; associated Legendre polynomials; universal central extensions; superelliptic Lie algebras; superelliptic curves; DJKM algebras; Fáa di Bruno's formula; Bell polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Bibliography; hypersurfaces in weighted projective space; K3-surfaces with double cyclic singularities K. Saito, Algebraic surfaces for regular systems of weights, to appear, preprint RIMS-563. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials symmetric power of a smooth projective curve; naive Grothendieck ring of varieties | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials second order derivative; differential uniformity; generic polynomials; density theorem; differential cryptanalysis; second order differential uniformity; inversion mapping | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials KP hierarchy; Jacobians; Riemann vanishing theorem; Schur-Weierstrass polynomials Bukhshtaber, VM; Ènol'skiĭ, VZ; Leĭkin, DV, Rational analogues of Abelian functions, Funct. Anal. Appl., 33, 83-94, (1999) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Hilbert's 17th problem; sum of squares of polynomials; convex cones M. Putinar and F.-H. Vasilescu, \textit{Positive polynomials on semialgebraic sets}, C. R. Math. Acad. Sci. Paris, 328 (1999), pp. 585--589. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials elliptic curves; torsion points; division fields; torsion fields; division polynomials; sporadic points; modular curves | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Zhegalkin polynomials; motives; dimer models; mirror symmetry | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials number of critical points of real polynomials; two variables Durfee, A., Kronenfeld, N., Munson, H., Roy, J. and Westby, I. (1993). Counting critical points of real polynomials in two variables. Amer. Math. Monthly 100 255-271. JSTOR: | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials existence of relative Bernstein polynomials; equisingularity H. Biosca, Caractérisation de l'existence de polynômes de Bernstein relatifs associés à une famille d'applications analytiques, C. R. Acad. Sci. Paris Sér. I Math. 325 (1997), no. 4, 395-398. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert calculus; equivariant \(K\)-theory; Grassmannians; genomic tableaux Pechenik, O., Yong, A.: Genomic tableaux and combinatorial \(K\)-theory. Discrete Math. Theor. Comput. Sci. Proc. \textbf{FPSAC'15}, 37-48 (2015) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials rationality of algebraic varieties; Grothendieck ring of varieties; motivic nearby fiber | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials rational normal scroll; Veronese embedding; join variety; multiprojective space; variety of complexes; variety of minimal degree; double structure; \(K3\) surface; Calabi-Yau scheme; Gorenstein ring; Gröbner basis | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Weierstrass points; Schubert index; moduli spaces of curves Eisenbud, D., Harris, J.: Recent progress in the study of Weierstrass points. Conf. Proceedings, Rome 1984. Lect. Notes Math. (to appear) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Drinfeld modules; heights; isogenies; modular polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double cosets; connected real semisimple Lie group; parabolic subgroup; flag manifold; complex semisimple Lie group Matsuki, T.: Orbits on flag manifolds. In: Proceedings of the International Congress of Mathematicians, Kyoto 1990, Vol. II. Springer, pp. 807-813 (1991) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials mechanical theorem proving in geometry; membership of the set of all polynomials | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials positive polynomials; sums of non-negative circuit polynomials; arithmetic-geometric exponentials; dual cone; \(\mathcal{S}\)-cone; second-order cone | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials \(K\)-theory; zeta function; \(K\)-theory of varieties; Grothendieck group of varieties; motivic measure | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials algebraic cycles; Grothendieck standard conjecture; threefolds С. Г. Танкеев, ``О стандартной гипотезе типа Лефшеца для комплексных проективных трехмерных многообразий'', Изв. РАН. Сер. матем., 74:1 (2010), 175 -- 196 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Quantum Schubert Calculus of homogeneous spaces; Pontryagin product, loop groups, Equivariant homology and cohomology of homogeneous spaces, Gromov-Witten invariants Leung, N. C.; Li, C., Gromov-Witten invariants for \(G / B\) and Pontryagin product for {\(\omega\)}\textit{K}, Trans. Amer. Math. Soc., 5, 2567-2599, (2012) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials decomposition of Hartshorne-Rao module; arithmetical Cohen-Macaulay scheme; liaison addition; arithmetically Buchsbaum schemes; double linkage; Hilbert functions | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Rényi-Erdős conjecture; Bertini theorem; polynomials with few terms | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert varieties; local complete intersection; pattern avoidance \beginbarticle \bauthor\binitsH. \bsnmÚlfarsson and \bauthor\binitsA. \bsnmWoo, \batitleWhich Scubert varieties are local complete intersections? \bjtitleProc. Lond. Math. Soc. (3) \bvolume107 (\byear2013), page 1004-\blpage1052. \endbarticle \endbibitem | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials constructivism; Galois theory; factorization of polynomials; splitting field; binary quadratic forms; composition of forms; Newton's polygon; genus; theorem of Riemann-Roch; Sylow's theorems [Edwards 2005] Edwards, H. \textit{Essays in Constructive Mathematics}. Springer-Verlag, New York. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials flatifying blowing-up; maximal Cohen Macaulay module; simultaneous partial resolution; small resolution; rational double point; RDP; matrix factorization; deformation of algebras; deformation of rational singularities; deformations of exceptional module; partial resolution; domination of resolution; contracting curves; strict transform; Wunram module; blowing up | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials canonical measures; Chebyshev polynomials; equidistribution; height; integral points; preperiodic points doi:10.1016/j.jnt.2010.10.003 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Kac-Moody Lie-algebra; ŜL\({}_ 2\); Kac-Moody group; parabolic subgroup; Weyl group; Schubert variety; standard monomials; tautological line bundle V. Lakshmibai and C. S. Seshadri, ?Thèorie monomiale standard pour \(\widehat{\mathfrak{s}\mathfrak{l}}_2 \) ,? C. R. Acad. Sci. Paris Ser. I,305, 183-185 (1987). | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double solids; irrationality problems; \(\mathbb Q\)-factoriality; potential density; elliptic fibration structures Cheltsov, Ivan; Park, Jihun, Sextic double solids. Cohomological and geometric approaches to rationality problems, Progr. Math. 282, 75-132, (2010), Birkh\H{a}user Boston, Inc., Boston, MA | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials quantum cohomology; Gromov-Witten invariants; Schubert calculus; small cohomology rings; homogeneous spaces; Pieri formulas Ionuţ Ciocan-Fontanine, On quantum cohomology rings of partial flag varieties, Duke Math. J. 98 (1999), no. 3, 485 -- 524. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Schubert calculus; cobordism; Grassmannian; generalized cohomology | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials elimination theory; discriminant of homogeneous polynomials; resultant of homogeneous polynomials; inertia forms Busé, L; Jouanolou, JP, On the discriminant scheme of homogeneous polynomials, Math. Comput. Sci., 8, 175-234, (2014) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials cell decomposition; double Bott-Samelson varieties Mouquin, V.: Cell decompositions of double Bott-Samelson varieties. Int. math. Res. not. 18, 8372-8410 (2015) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials linear projections; double point; ramification schemes | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials topological invariants of algebraic varieties; homology groups; fundamental groups; Alexander polynomials; Hodge structures; Whitney stratifications; plane curve and normal surface singularities; Milnor fibration; lattice for an isolated hypersurface singularity; integral bilinear forms; weighted projective varieties; mixed Hodge structures; hypersurface complements; cohomology of complete intersections A. Dimca, ''Singularities and Topology of Hypersurfaces'', Universitext, Springer-Verlag, New York, 1992. DOI: 10.1007/978-1-4612-4404-2 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials coherent sheaves; finite length modules; Grothendieck ring of varieties; Hilbert scheme of points; torus actions | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials cubic surfaces; double line; projections; branch loci; resolvent surfaces; fundamental groups; projective plane Faenzi, D.: A remark on Pfaffian surfaces and aCM bundles. In: Vector Bundles and Low Codimensional Subvarieties: State of the Art and Recent Developments, vol. 21 of Quad. Mat. pp. 209-217. Dept. Math., Seconda Univ. Napoli, Caserta (2007) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double-periodic-in-\(t\) solutions; finite-gap solutions; nonlinear Schrödinger equation A. O. Smirnov, Solutions of the nonlinear Schrödinger equation that are elliptic in \?, Teoret. Mat. Fiz. 107 (1996), no. 2, 188 -- 200 (Russian, with English and Russian summaries); English transl., Theoret. and Math. Phys. 107 (1996), no. 2, 568 -- 578. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials polynomials constant on a hyperplane; CR mappings of spheres and hyperquadrics; monomial mappings; degree estimates; Newton diagram Lebl, J., Peters, H.: Polynomials constant on a hyperplane and CR maps of hyperquadrics. arXiv: 0910.2673 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials double cover; hyperelliptic surface of general type; hyperelliptic fibration; fundamental group; slope; singularities | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials plane curve; inflection point; bitangency; double point; triple point F. S. Dias and L. F. Mello,Geometry of plane curves. Bull. Sci. Math. 135 (2011),333--344. DOI: 10.1016/j.bulsci.2011.03.007 | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials b-function; D-modules; Weyl algebra; Bernstein-Sato polynomials; hyperplane arrangements; tame arrangements; free divisors; Euler-homogeneous divisors; Saito-holonomic divisors; logarithmic differential forms; logarithmic vector fields; Spencer complex | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Teichmüller groupoids; Galois action; Grothendieck conjecture Ichikawa, Teichmüller groupoids and Galois action, J. Reine Angew. Math. 559 pp 95-- (2003) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Eisenstein symbol map; motivic cohomology; Néron model; Bernoulli polynomials; boundary maps; K-theory; place of bad reduction; elliptic curve; modular curve Schappacher, N.; Scholl, A. J., \textit{the boundary of the Eisenstein symbol}, Math. Ann., 290, 303-321, (1991) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials global sections; line bundles; Schubert varieties; root systems; Weyl groups R. Dabrowski, A simple proof of a necessary and sufficient condition for the existence of nontrivial global sections of a line bundle on a Schubert variety, in: Kazhdan-Lusztig Theory and Related Topics (Chicago, IL, 1989), Contemp. Math., Vol. 139, Amer. Math. Soc., Providence, RI, 1992, pp. 113-120. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials determinantal ideals; algebras with straightening law; Hodge algebras; Schubert cycles; divisor class groups W. Bruns, U. Vetter, \(Determinantal Rings\). Lecture Notes in Mathematics, vol. 1327 (Springer, New York, 1988) | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials permutation pattern avoidance; Schubert varieties | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials category of fields; duality for local fields; Grothendieck topologies | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials elliptic curves; division polynomials; elliptic divisibility sequences | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials sine square deformation; SUSY quantum mechanics; orthogonal polynomials K. Okunishi and H. Katsura, Sine-square deformation and supersymmetric quantum mechanics, . | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Grothendieck's dessins d'enfants; quantum contextuality; finite geometries M. Planat, A. Giorgetti, F. Holweck and M. Saniga, Quantum contextual finite geometries from dessins d'enfants, Int. J. Geom. Methods Mod. Phys. 12 (2015), 1550067, 10.1142/ s021988781550067x. | 0 |
Grothendieck polynomials; Schubert polynomials; double Schubert polynomials Flag variety; Schubert variety; sagbi basis; Gelfand-Tsetlin pattern; Borel-Weil theorem Kogan, M., Miller, E.: Toric degeneration of Schubert varieties and Gelfand--Tsetlin polytopes. Adv. Math. 193(1), 1--17 (2005) | 0 |
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