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

3 votes
1 answer
310 views

When the affine quotient is faithfully flat?

It may be easy for the expert. Consider the map from $n$ by $m$ matrices (over $\mathbb{C}$ )to the $n$ by $n$ symmetric matrices $\phi\colon A\mapsto A A^T$. My question is when this map is faithf …
Jia-jun Ma's user avatar
6 votes
1 answer
1k views

Is $k[X]^G$ integral closed in $k[X]$.

May assume field $k=\mathbb{C}$. Let $X$ be an affine variety and $G$ be a reductive group (may assume connected). Is the ring of invariants $k[X]^G$ integral closed in $k[X]$? The claim may not t …
Jia-jun Ma's user avatar