All Questions
10 questions
1
vote
0
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156
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Software for computing invariant rings
I have an linearly reductive algebraic group $G$ acting regularly on an affine variety $X$(over an algebraically closed field of characteristic 0). I want to compute the invariant ring $\mathbb{K}[X]^{...
- 839
1
vote
0
answers
80
views
When is $Y$ not an orbit closure?
Let $G$ be a linearly reductive algebraic group acting regularly on an affine space over $\mathbb{A}^n$ an algebraically closed field $\mathbb{K}$. Let $Y$ be a $G$-invariant (closed) affine ...
- 839
1
vote
0
answers
208
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Is $\langle\chi,\lambda\rangle=0$, whenever the limit exists? Where is the mistake?
Suppose $G$ is a linearly reductive algebraic group acting linearly on a finite dimensional vector space $V$ over $\mathbb{C}$. This induces an action on the coordinate ring $\mathbb{C}[V]$ (see here)....
- 839
1
vote
0
answers
362
views
Invariant ring of linear algebraic groups
Let $G$ be a connected linear algebraic group. This question concerns Hilbert's 14th Problem for the adjoint action of $G$ on itself. Let $k[G]^G$ denote the algebra of regular functions on $G$ ...
- 2,751
3
votes
0
answers
147
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A good stratification of a variety on which an algebraic group acts
Let $X$ be an algebraic variety over an algebraically closed field $k$ of characteristic 0
(a reduced separated scheme of finite type over $k$).
Let $G$ be a connected linear algebraic group over $k$ (...
- 14.2k
2
votes
0
answers
104
views
Alternatives to the ring of invariants depicting the orbit closures?
Let $G$ be an affine algebraic group over $\mathbb{C}$ and $V=\textrm{Spec}(A)$ an affine $G$-variety. Assume that $G$ is reductive. My understanding is that a central object in studying the action of ...
- 3,031
3
votes
0
answers
140
views
Topological criterion for GIT semistability
Let $X$ be a complex algebraic variety and $G$ a complex reductive group acting on $X$. Let $L$ be a linearization of this action, i.e. a line bundle with a linear action of $G$ covering that of $X$. ...
- 31
4
votes
0
answers
119
views
Invariants and subgroups
Let $G$ be an affine algebraic group over some algebraically closed field $K$, and let $H$ be a closed subgroup.
Assume that $G$ acts algebraically on an affine variety $X$.
Assume that $X'\subseteq ...
- 5,039
3
votes
0
answers
325
views
Ring of invariants and Borel subgroup
Let $G$ be a connected algebraic group (can assume $G$ to be reductive) acting on a $k$-algebra $A$. Let $B$ be a Borel subgroup of $G$.
Q. Is it generally true that the the ring of invariants $A^...
- 113
9
votes
1
answer
346
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Standard Monomial basis for other types
For the algebraic group $SL_n$ (type $A_{n-1}$) and for a dominant weight $\lambda$ the standard monomials are indexed by the semi-standard young tableaux of shape $\lambda$ and they form a basis for ...
- 213