All Questions
7 questions with no upvoted or accepted answers
8
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636
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Chern Classes of Exterior Products of a vector bundle.
This is mostly a question in combinatorics. Is there a clean way in terms of determinantal identities to write down $c(\wedge^k V)$ i.e. the individual summands in terms of the individual summands of $...
- 327
6
votes
0
answers
455
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Cohomology of Bott-Samelson varieties?
How is the cohomology of Bott-Samelson varieties (desingularizations of Schubert Varieties ) usually calculated? Let's fix the Lie group to be $GL_n(\mathbb{C})$ or $SL_n(\mathbb{C})$ here.
Is there ...
- 1,719
5
votes
0
answers
171
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Spinor representation for $\operatorname{Spin}(V \oplus V^*)$
I'm studding Hitchin's Generalized Calabi-Yau Manifolds https://arxiv.org/abs/math/0209099 and I've stuck here:
Suppose that $V$ is a vector space and denote its dual by $V^*$. Now we know that the $\...
5
votes
0
answers
584
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What exactly is a coherent $G$-sheaf?
On page 69 in Mumford's Abelian Varieties book, he says:
"Let $G$ be a finite group acting on a variety $X/k$, and let $X\stackrel{\pi}{\longrightarrow} Y := X/G$ be the quotient. Let $\mathcal{F}$ ...
- 7,527
3
votes
0
answers
249
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Grothendieck schemes and the Sheffer differential op calculus (Rota, Roman, et al. finite operator calculus)
In "Left differential operators on non-commutative algebras" on p. 4, Michiel Hazewinkel displays "precisely the right definition of differential operator" as
$$D\; X^n = F(\tfrac{...
- 10.5k
3
votes
0
answers
150
views
Integral Homology of GIT Quotients
Is there any example of GIT quotients of linear actions on a Euclidean space ${\mathbb C}^n$ that satisfy the following conditions?
The quotient is compact and smooth.
The homology of the quotient ...
- 1,207
2
votes
0
answers
169
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The dimension of the representation ring
Let $G$ be a compact Lie group. I am trying to characterize the algebraic properties of the representation ring $R(G)$ of $G$. In the case of the $n$-torus, the representation ring $R(T)$ is ...
