Questions tagged [perverse-sheaves]
The perverse-sheaves tag has no usage guidance.
206 questions
4
votes
1
answer
639
views
Morphisms between pure complexes of sheaves
I would like to understand the theory of pure complexes of (etale?) sheaves (of geometric origin?). In particular, I would like to understand which conditions are realy necessary in (part 1 of) ...
- 6,162
7
votes
1
answer
884
views
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 $\lambda \in A^1$ ...
- 45.7k
11
votes
2
answers
2k
views
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 ...
- 3,131
13
votes
4
answers
3k
views
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 ...
CommunityBot
- 1
24
votes
2
answers
4k
views
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 ...
CommunityBot
- 1
5
votes
1
answer
766
views
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 \...
- 4,949