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9 votes
0 answers
335 views

Understanding the mixed Hodge structure on D-modules on $\mathbb{C}$

Consider the category of regular D-modules on $\mathbb{C}$ (let's say as a complex manifold). It's a well-known fact that if you consider the subcategory of these where the singular support is the ...
Ben Webster's user avatar
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3 votes
1 answer
312 views

Iterating specialization of sheaves?

This is a question about the operation of taking the specialization of sheaves along a subspace. I'll recall the settings in which I've encountered a notion of specialization of sheaves: The real, ...
Mathmank's user avatar
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6 votes
0 answers
216 views

BRST cohomology and vanishing cycles

Consider the $\mathbb{C}$-variety $\mathbb{A}^{1}$, equipped with the potential (ie global function) $P:=\frac{z^{n+1}}{n+1}$. We can form the twisted de Rham complex $H_{dR}(\mathbb{A}^{1},P)$ which ...
user avatar
4 votes
1 answer
511 views

Nearby cycles and specialisation - properties

I am looking for reference for properties of nearby cycles - specifically, commutation with non-characteristic pull-back (good enough - commutation with pull-back to closed subvariety which is ...
Sasha's user avatar
  • 5,562