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Results tagged with invariant-theory
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user 391
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.
2
votes
Checking smoothness of the components of a highly symmetric scheme via quotient?
You apparently mean the action on the set of components is free, not just faithful.
For $C$ a component of $X$, the composite map $C \to X \to X//G$ is a finite map, and (by the freeness assumption) …
- 27.9k
15
votes
Quotients by the additive group $\mathbb G_a$
In general, the only definition I know of GIT quotient is $Proj$ of the invariant ring. The obvious statements one can make about the rational map $Proj\ R\to Proj\ R^G$ are that it collapses $G$-orbi …
- 27.9k
5
votes
Accepted
Left U_n-invariants of SL_n - an exercise in Kraft-Procesi
No, they don't. $U_n(K)$ is performing upward row operations, so any $m\times m$ minor that uses the last $m$ rows will be $U_n(K)$-invariant, e.g. any single bottom entry. You won't be able to genera …
- 27.9k