Questions tagged [perverse-sheaves]
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206 questions
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Localization of vanishing cycles
Consider a regular holonomic D-module (or a perverse sheaf) $M$ on a smooth variety $X$. Let $f:X\to A^1$ be a polynomial (or holomorphic) function.
Question: Is it true that the $\lambda \in A^1$ ...
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What do the local systems in Lusztig's perverse sheaves on quiver varieties look like?
In "Quivers, perverse sheaves and quantized enveloping algebras," Lusztig defines a category of perverse sheaves on the moduli stack of representations of a quiver. These perverse sheaves are defined ...
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Why is the decomposition theorem awesome?
I saw the statement of the decomposition theorem for perverse sheaves sometime ago. I know that (modulo most of the details) it implies some big theorems in algebraic geometry and gives new proofs for ...
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Hypercube decomposition of perverse sheaves
There is a well known theorem that says that the functor associating to a perverse sheaf $F$ on $X$ the data $(F|_U,\phi_f(F),can:\psi_f(F) \to \phi_f(F),var:\phi_f(F)\to \psi_f(F)(-1))$ where $U = X \...
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Examples for Decomposition Theorem
There's an important piece of geometric knowledge usually quoted as Beilinson-Bernstein-Deligne.
Here's a refresher: by $IC$ one means the intersection complex, which is just $\mathbb Q$ for a smooth ...
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How to do Computations Using the Decomposition Theorem for Perverse Sheaves
This is a follow-up to this post on the Decomposition Theorem. Hopefully, this will also invite some discussion about the theorem and perverse sheaves in general.
My question is how does one use the ...
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