The nil Hecke ring and singularity of Schubert varieties

DOI10.1007/s002220050038zbMath0863.14031arXivalg-geom/9503015OpenAlexW4239506166MaRDI QIDQ1922550

Shrawan Kumar

Publication date: 5 November 1996

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/alg-geom/9503015

zbMATH Keywords

singularitySchubert varietiesnil Hecke ringsmoothness of points

Mathematics Subject Classification ID

Grassmannians, Schubert varieties, flag manifolds (14M15) Linear algebraic groups over the reals, the complexes, the quaternions (20G20) Lie algebras of linear algebraic groups (17B45)

Related Items (33)

Specializations of Grothendieck polynomials ⋮ Singularities of Generalized Richardson Varieties ⋮ Springer fibers and Schubert points ⋮ Tangent cones to Schubert varieties in types \(A_{n}\), \(B_{n}\) and \(C_{n}\) ⋮ Billey-Postnikov decompositions and the fibre bundle structure of Schubert varieties ⋮ Equivariant Chow groups for torus actions ⋮ Local Hodge theory of Soergel bimodules ⋮ Schubert varieties and short braidedness ⋮ Affine nil-Hecke algebras and quantum cohomology ⋮ G-valued crystalline deformation rings in the Fontaine–Laffaille range ⋮ Geometric properties of the Kazhdan-Lusztig Schubert basis ⋮ \({\mathbb{G}_a^M}\) degeneration of flag varieties ⋮ Smooth Schubert varieties in \(G/B\) and \(B\)-submodules of \(\mathfrak{g}/\mathfrak{b}\) ⋮ Smoothness of Schubert varieties in twisted affine Grassmannians ⋮ On tangent cones to Schubert varieties in type \(E\) ⋮ Parity sheaves, moment graphs and the \(p\)-smooth locus of Schubert varieties ⋮ Littlewood-Richardson coefficients for reflection groups. ⋮ Chern class of Schubert cells in the flag manifold and related algebras ⋮ Smooth Schubert varieties in the affine flag variety of type \(\tilde{A}\) ⋮ Kostant-Kumar polynomials and tangent cones to Schubert varieties for involutions in \(A_{n}\), \(F_{4}\), and \(G_{2}\) ⋮ Smooth and palindromic Schubert varieties in affine Grassmannians ⋮ The minimal degeneration singularities in the affine Grassmannians ⋮ Degenerate coordinate rings of flag varieties and Frobenius splitting ⋮ On cones tangent to Schubert varieties of type $D_n$ ⋮ Classes d'Euler équivariantes et points rationnellement lisses. (Equivariant Euler classes and rationally smooth points.) ⋮ Good and semi-stable reductions of Shimura varieties ⋮ Pattern avoidance and rational smoothness of Schubert varieties ⋮ Poisson harmonic forms, Kostant harmonic forms, and the \(S^1\)-equivariant cohomology of \(K/T\) ⋮ The incidence class and the hierarchy of orbits ⋮ Smoothness of Schubert varieties via patterns in root subsystems ⋮ Rational smoothness and fixed points of torus actions ⋮ Schubert calculus and the homology of the Peterson variety ⋮ Excited Young diagrams, equivariant $K$-theory, and Schubert varieties

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