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Questions tagged [geometric-invariant-theory]

for questions on geometric invariant theory (or GIT), including stability criteria and symplectic quotients.

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Quotient $(V -S)/G$ is a quasi-projective variety for every closed $S \subset V$ with free $G$-action

I have a question about the statement of Remark 1.4 following on Thm 1.3 from Burt Totaro's paper "The Chow Ring of a Classifying Space" (p. 4): Let $G$ be a reductive group over a field $k$....
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Equivalence between coactions and actions plus a linearization line bundle

Let $G$ be an algebraic group over a field $k$, and $\mathbb{P}(V)$ is a projective space. Then Mumford said in his book Geometric Invariant Theory that there's a equivalence between the set of all ...
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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 $\Phi \colon M \to \mathfrak{g^*}$ ...
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Invariant Polynomes under group action - given the invariants looking for the group. algorithmic solution?

I have given a finite set $S$ of polynomes in the ring $R = C[x_1,\dots,x_n]$. I need to know the minimal group $G$ wich acts on $R$ such that $C[S]$ is the ring of invariants of $R$ under the action ...
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