4
votes
1answer
178 views

Smooth mixed hodge modules - representations of fundamental group?

I do not know much about mixed Hodge modules. I would like to ask: Let $X$ be a smooth connected algebraic complex variety, with a chosen point. Could one describe smooth mixed Hodge modules on $X$ as ...
1
vote
0answers
102 views

The associated graded of a mixed Hodge module

Unfortunately this question will be a bit vague, since the question revolves around a memory of something I may have heard in a talk (long time ago). Let $X$ be a smooth complex variety. Let $MHM(X)$ ...
3
votes
1answer
347 views

Polarizable variations of (mixed) Hodge structures

I am trying to come to grips with Saito's theory of mixed Hodge modules (slightly) beyond just the basic axiomatic formalism. I will take my Hodge structures and sheaves to be rational, but I would be ...
5
votes
0answers
299 views

Blow ups and Characteristic varieties

Let $f:Y\to X$ be a morphism of smooth varieties (complex analytic or algebraic as you wish). We have $$ T^* Y \overset{f_d}{\longleftarrow} Y\times_X T^*X \overset{f_\pi}{\longrightarrow} T^* X ...
5
votes
1answer
673 views

Relation between holonomic D-modules and perverse sheaves

Given a smooth complex algebraic variety, the Riemann-Hilbert-correspondence tells us, that the category of perverse sheaves is equivalent to the category of regular, holonomic D-modules. However not ...
6
votes
1answer
454 views

How does one interpret the naive t-structure on constructible sheaves as a t-structure on D-modules?

By the Riemann-Hilbert correspondence, there is an equivalence between (1) $\mathcal{D}\operatorname{-mod}(X)$ , the (derived) category of holonomic D-modules on a complex variety X, and (2) ...
6
votes
1answer
896 views

Computation of vanishing cycles

Here's the problem I'm looking at: $F$ is a perverse sheaf (or a regular holonomic D-module, or even a mixed hodge module) on $\mathbb{C}^2$ stratified by $z_1 = 0$, $z_2=0$. It can be caracterized ...
7
votes
4answers
1k views

Gluing perverse sheaves?

It might be a stupid question. How to glue perverse sheaves? I am considering the following example. Flag variety of $sl_2$, which is $P^1$. Consider category of perverse sheaves on $P^1$. Denoted ...
6
votes
1answer
679 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 $\lambda \in A^1$ ...