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Results tagged with geometric-invariant-theory
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user 43639
for questions on geometric invariant theory (or GIT), including stability criteria and symplectic quotients.
1
vote
Bad Categorical Quotients
Let me explain slightly modified example 4.6 by A'Campo-Neuen and Hausen.
Suppose that $\mathbb C^*$ acts on $X=\mathbb P^1_{x_1:x_2} \times \mathbb A^2_{y, z}$ (indices denote corresponding coordina …
- 1,980
0
votes
Accepted
Supposed generalization of $X/(G \times H)\simeq (X/G)/H$ for GIT-quotients
My question should have consisted of two. I will formulated both using linearization via line bundles, not embeddings into projective space, as it makes them more clear.
Question 1. Suppose that $\pi …
- 1,980
5
votes
1
answer
314
views
Supposed generalization of $X/(G \times H)\simeq (X/G)/H$ for GIT-quotients
I wonder whether it is true that the composition of two GIT-quotients is another GIT-quotient. It should be an analogue of a set-theoretic formula $X/(G \times H)\simeq (X/G)/H$ but with GIT-quotients …
- 1,980
4
votes
1
answer
619
views
Vector bundles on quotient variety
Let an algebraic group $G$ act on a complex variety $X$ such that there is a good enough quotient $X/G$ (for example, $G$ acts on a vector space $V$ linearly and $X=V_{ss}$ is a variety of semi-stable …
- 1,980
18
votes
1
answer
3k
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Why is Mumford's GIT-quotient so effective?
According to remark 6.14 in Shigeru Mukai's An introduction to invariants and moduli (unfortunately, the page is not available on Google Books, so I explain it below), the GIT-quotient of an affine va …
- 1,980