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Results tagged with invariant-theory
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user 16762
Invariant theory deals with an algebraic, geometric or analytic structure $X$, submitted to the action of an (algebraic) group $G$. It studies $G$-invariant elements of $X$ as well as the set of $G$-orbits.
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 …
- 396
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 …
- 1,645