Perverse sheaves on rank stratifications

DOI10.1215/S0012-7094-99-09609-6zbMath0958.14009MaRDI QIDQ1974882

Tom Braden, Mikhail Grinberg

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

stratified spacesperverse sheavesrepresentations of a quiverhypercohomology groupsmicrolocal perverse sheaves

Mathematics Subject Classification ID

Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials (14F10) Other algebro-geometric (co)homologies (e.g., intersection, equivariant, Lawson, Deligne (co)homologies) (14F43) Stratifications; constructible sheaves; intersection cohomology (complex-analytic aspects) (32S60)

Related Items (21)

Perverse sheaves over real hyperplane arrangements ⋮ Perverse sheaves, Koszul IC-modules, and the quiver for the category \(\mathcal{O}\) ⋮ \(\mathcal{D}\)-modules on representations of Capelli type ⋮ On a class of holonomic \(\mathcal D\)-modules on \(M_n(\mathbb C)\) related to the action of \(\mathrm{GL}_n(\mathbb C)\times \mathrm{GL}_n (\mathbb C)\) ⋮ Characters of equivariant -modules on spaces of matrices ⋮ Categories of bounded \((\mathfrak{sp}(\mathrm{S}^2V\oplus\mathrm{S}^2V^\ast)\), \(\mathfrak{gl}(V))\)- and \((\mathfrak{sp}(\Lambda ^2 V\oplus\Lambda ^2V^\ast)\), \(\mathfrak{gl}(V))\)-modules ⋮ On category \(\mathcal O\) over triangular generalized Weyl algebras. ⋮ Iterated local cohomology groups and Lyubeznik numbers for determinantal rings ⋮ Recollement for perverse sheaves on real hyperplane arrangements ⋮ Equivariant D-modules on binary cubic forms ⋮ Unnamed Item ⋮ On categories of equivariant \(\mathcal{D}\)-modules ⋮ \({\mathcal D}\)-modules associated to the determinantal singularities ⋮ Algebraic description of \(\mathcal D\)-modules associated to \(3\times 3\) matrices. ⋮ \(\mathcal D\)-modules associated to the projective space of \(n\times n\) matrices. ⋮ On the reducibility of characteristic varieties ⋮ Stacks similar to the stack of perverse sheaves ⋮ Perverse sheaves on smooth toric varieties ⋮ Witt groups of abelian categories and perverse sheaves ⋮ Exit paths and constructible stacks ⋮ WHEN ARE THERE ENOUGH PROJECTIVE PERVERSE SHEAVES?

Cites Work

• Morse homology
• The invariant holonomic system on a semisimple Lie algebra
• Elementary construction of perverse sheaves
• Simple singularities and simple algebraic groups
• Supersymmetry and Morse theory
• Perverse sheaves on affine Grassmannians and Langlands duality
• Sheaves on a loop group and Langlands duality
• A microlocal version of the Riemann-Hilbert correspondence
• Perverse sheaves and quivers
• Nondegenerate critical manifolds
• Quivers, Perverse Sheaves, and Quantized Enveloping Algebras
• Introduction to microlocal analysis
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