Rational smoothness and fixed points of torus actions

DOI10.1007/BF01237356zbMath0953.14004MaRDI QIDQ1306578

Michel Brion

Publication date: 23 January 2001

Published in: Transformation Groups (Search for Journal in Brave)

zbMATH Keywords

fixed pointsalgebraic groupslocal cohomologytorus actionsslicesrational smoothness

Mathematics Subject Classification ID

Homogeneous spaces and generalizations (14M17) Geometric invariant theory (14L24) Group actions on varieties or schemes (quotients) (14L30) Local cohomology and algebraic geometry (14B15)

Related Items (32)

\(K\)-orbit closures on \(G/B\) as universal degeneracy loci for flagged vector bundles splitting as direct sums ⋮ Closures of 𝐾-orbits in the flag variety for 𝑆𝑈*(2𝑛) ⋮ Betti Numbers of Toric Varieties and Eulerian Polynomials ⋮ Descent systems for Bruhat posets ⋮ Convex polytopes for the central degeneration of the affine Grassmannian ⋮ \(K\)-orbit closures on \(G/B\) as universal degeneracy loci for flagged vector bundles with symmetric or skew-symmetric bilinear form ⋮ Rational smoothness, cellular decompositions and GKM theory ⋮ Cominuscule points and Schubert varieties ⋮ Rationally smooth algebraic monoids. ⋮ Graham's variety and perverse sheaves on the nilpotent cone ⋮ Unramified affine Springer fibers and isospectral Hilbert schemes ⋮ GKM-theory for torus actions on cyclic quiver Grassmannians ⋮ On intersection cohomology with torus actions of complexity one ⋮ On the Borel submonoid of a symplectic monoid ⋮ On the multiplicity spaces of spherical subgroups of minimal rank ⋮ Homogeneous coordinate rings as direct summands of regular rings ⋮ Algebraic rational cells and equivariant intersection theory ⋮ Generalized moment graphs and the equivariant intersection cohomology of BXB-orbit closures in the wonderful compactification of a group ⋮ The \(H\)-polynomial of an irreducible representation. ⋮ Rational smoothness of varieties of quiver representations. ⋮ Intersection cohomology of pure sheaf spaces using Kirwan's desingularization ⋮ Criteria for rational smoothness of some symmetric orbit closures. ⋮ Polynomials for \(\mathrm{GL}_p\times \mathrm{GL}_q\) orbit closures in the flag variety ⋮ Closures of On-Orbits in the Flag Variety for GLn ⋮ Equivariant cohomology of rationally smooth group embeddings ⋮ Equivariant perverse sheaves and quasi-hereditary algebras ⋮ Decomposition theorem and torus actions of complexity one ⋮ Orbits of strongly solvable spherical subgroups on the flag variety ⋮ Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety ⋮ \(\mathsf{K}\)-orbit closures and Barbasch-Evens-Magyar varieties ⋮ Parametrization, structure and Bruhat order of certain spherical quotients ⋮ Intersection cohomology of \(B\times B\)-orbit closures in group compactifications.

Cites Work

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• The Bruhat order on symmetric varieties
• Vanishing of odd-dimensional intersection cohomology
• Representations of Coxeter groups and Hecke algebras
• Classes d'Euler équivariantes et points rationnellement lisses. (Equivariant Euler classes and rationally smooth points.)
• Analogue of the Bruhat-Chevalley order for reductive monoids
• The behavior at infinity of the Bruhat decomposition
• Equivariant completion
• The nil Hecke ring and Deodhar's conjecture on Bruhat intervals
• Cohomology of regular embeddings
• On Zariski tangent spaces of Schubert varieties, and a proof of a conjecture of Deodhar
• The nil Hecke ring and singularity of Schubert varieties
• On orbits of algebraic groups and Lie groups

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