All Questions
Tagged with geometric-invariant-theory sg.symplectic-geometry
8 questions
2
votes
0
answers
33
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Kähler quotients for generic $\xi\in \mathfrak{g}^*$
In this question I intentionally omit words like "(non)compact" because I am not sure about the precise setting where this question makes sense.
Let $M$ be a symplectic manifold, $G$ a Lie ...
- 1,488
5
votes
1
answer
438
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A criterion for orbits of complex reductive group to be closed
I am having some trouble understanding Nakajima's proof of the Kempf-Ness theorem in [1]. At the end (proof of Proposition 3.9(6)), his argument is basically the following:
Let $G=K_{\Bbb C}$ be a ...
- 779
7
votes
0
answers
466
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Kähler quotients of affine varieties and GIT
Let $X\subseteq \Bbb C^n$ be a smooth affine variety and $G=K_{\Bbb C}$ a complex reductive group acting linearly on $\Bbb C^n$ preserving $X$ (where $K$ is a maximal compact subgroup of $G$). Suppose ...
- 779
0
votes
0
answers
101
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G-invariant functions on manifold for G compact
In a paper I saw the following statement:
Let $M$ be a connected symplectic manifold and $G$ be a compact Liegroup acting symplectically and hamiltonian on $M$. Let $\Phi \colon M \to \mathfrak{g^*}$ ...
- 501
2
votes
2
answers
2k
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Semistability in GIT
If I understand correctly, in geometric invariant theory, polystable points can be defined as those which have a closed orbit. Is it true that semistable points can be characterized as those whose ...
- 1,347
5
votes
2
answers
1k
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A question about Marsden-Weinstein reduction theory
Let $G$ be a compact Lie group and $\frak g$ be its Lie algebra. Then by Marsden-Weinstein reduction theory we know that if we take $M=T^*G$ and $J \colon M\to \frak g^*$ be its moment map then the ...
user21574
8
votes
3
answers
3k
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Why can we define the moment map in this way (i.e. why is this form exact)?
Given a symplectic manifold $(X, \omega)$ and a group $G$ acting on $X$ preserving the symplectic form, we define the moment map $\mu : X \to \mathfrak{g}^*$ so that
$$
\langle d\mu(v), \xi\rangle = \...
- 6,290
10
votes
2
answers
1k
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Fukaya categories of hyperkahler reductions: general request for information
I'd really like to hear any references or information people have about the Fukaya categories of hyperkahler reductions of vector spaces (for more informations on the varieties, see Nick Proudfoot's ...
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