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Results tagged with d-modules
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user 78824
Modules over rings of differential operators.
7
votes
1
answer
478
views
How can I construct D-modules over projective space using explicit differential equations?
Over $\mathbb{A}^n$, it is easy to construct D-modules by writing down an explicit linear system of PDE's and then writing a presentation of the associated D-module
$$
\mathcal{D}^n \xrightarrow{} \ma …
- 1,716
2
votes
0
answers
220
views
What techniques are available for constructing D-modules over smooth projective varieties?
I'm trying to learn about D-modules for computing intersection cohomology but I'm having trouble coming up with explicit constructions of D-modules on projective varieties. Since this is an involved p …
- 1,716
9
votes
2
answers
806
views
What is integration along the fibers in D-module theory?
In Hotta, Takeuchi, Tanisaki's book on "D-modules, Perverse Sheaves, and Representation theory", for a morphism of smooth algebraic varieties $f:X \to Y$, they use the notation
$$
\int_f:D^b(D_X^{op}) …
- 1,716
23
votes
2
answers
2k
views
What are examples of D-modules that I should have in mind while learning the theory?
I've been reading about D-modules this summer in preparation for a learning seminar on intersection cohomology. Unfortunately, many of the ideas are not sticking while I learn about the theory. What a …
- 1,716
4
votes
What are examples of D-modules that I should have in mind while learning the theory?
I will edit this question as I learn more, but here's one useful example: Consider the $\mathcal{D}_{\mathbb{A}^1}$-module
$$
\frac{\mathcal{D}_{\mathbb{A}^1}}{\mathcal{D}_{\mathbb{A}^1}(t\partial_t - …
- 1,716
17
votes
2
answers
1k
views
What is the motivation behind the characteristic variety of a D-module and what does it's ge...
Given a smooth algebraic variety $X$, and an $\mathcal{M}\in \text{Mod}(D_X)$, there is the characteristic variety of $\mathcal{M}$ defined as
$$
\text{Char}(\mathcal{M}):= V\left(\sqrt{Ann(\mathcal{M …
- 1,716