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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.

3 votes
0 answers
112 views

Local cohomology with coefficients in ideals of parameters

I'm not an expert in local cohomology, but the following problems have come up in my work, and I'd like to get a sense of where things stand. Let $\mathbb{A}^n=\operatorname{Spec} \mathbb{C}[x_1, \dot …
Marc Besson's user avatar
5 votes
Accepted

Question on geometric invariant theory

I believe this is addressed on page 52, underneath the statement of Iwahori's theorem. He provides an argument for why Iwahori's result can be strengthened to G reductive by considering $G \rightarrow …
Marc Besson's user avatar
3 votes
0 answers
173 views

Intersection homology of toric resolutions

I'm interested in the intersection homology of toric varieties associated to a polytope $P$ with proper faces F, and a subdivision $P'$ of P. Let $X_P$ be the toric variety associated to the polytope …
Marc Besson's user avatar
6 votes
1 answer
291 views

Real forms of complex reductive groups

I have a collection of related (to me) questions, which stem from the fact that I feel like I have a bunch of pieces, but not a full clear picture. I'm curious about forms of reductive groups in gener …
Marc Besson's user avatar
9 votes
0 answers
471 views

What is wrong with $A^{(2)}_{2n}$?

When dealing with affine Kac-Moody groups, especially geometrically (e.g. by examining their affine flag varieties or affine Grassmannians) I've been taught that time and time again, issues arise in t …
Marc Besson's user avatar
4 votes
0 answers
138 views

Singular schemes with a torus action and embedded points

I've got a couple rather geometric questions about the following setup. Let $X$ be a scheme over an algebraically closed field ($\mathbb{C}$, say) with the action of a torus $T$, such that the action …
Marc Besson's user avatar
8 votes
1 answer
578 views

Convolution in K-Theory via an Example (From StackExchange)

I've spent lots of time in Chriss and Ginzburg's "Complex Geometry and Representation Theory" and despite convolution (in Borel-Moore homology or K-theory) being very central, I feel like I'm still la …
Marc Besson's user avatar
2 votes
1 answer
339 views

A question on some lemmas in Orlov's "Triangulated Categories of Singularities and D-Branes ...

I'll write the two lemmas I have questions about, and then ask my questions. For reference, I'm using the following definition of Gorenstein: $\mathbf{Definition\ 1.15}$ A local noetherian ring $A$ i …
Marc Besson's user avatar