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3 votes
0 answers
127 views

Orbit space of the action of $\mathrm{GL}(V)$ on the Grassmannian of $V\wedge V$

$ \newcommand{\K}{\mathbb{K}} \newcommand{\R}{\mathbb{R}} \newcommand{\C}{\mathbb{C}} \newcommand{\N}{\mathbb{N}} \DeclareMathOperator{\GL}{GL} \DeclareMathOperator{\Grass}{Grass} $Consider $\K\in\{\R,...
Seba's user avatar
  • 126
0 votes
1 answer
683 views

Self duality and anti-self duality of Weyl curvature in four dimension

I am trying to compute explicitly in terms of extrinsic curvature the self dual part $W^+$ and the anti-self dual part $W^-$ of the Weyl tensor $W$ associated with a codimension 1 submanifold into ...
Pete09's user avatar
  • 11
1 vote
1 answer
351 views

GIT quotients of open subsets

Let X be a projective variety on with a action of reductive group G. Let L be a G Linearised ample line bundle on X. Let U be a G stable open subset of X. Let $U^{ss}:=X^{ss}\cap U$. Is it true that $...
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2 votes
1 answer
721 views

lines in projective spaces [closed]

Let $\{v_1,v_2, \cdots , v_n, w_1,w_2, \cdots ,w_n\}$ be a basis of $\mathbb C^{2n}$. For a $n$-dimensional subspace $V \in Gr(n,\mathbb C^{2n})$ define another $n$ dimensional subspace $\bar{V} \in ...
Mark's user avatar
  • 185
5 votes
0 answers
278 views

Smooth quotients and separation of orbits

Consider a unipotent algebraic group $G$ over $\mathbb{C}$ acting polynomially on $\mathbb{C}^n$. Suppose that the quotient exists as an analytical geometric quotient, i.e., $\mathbb{C}^n/G$ is a ...
Yoyo's user avatar
  • 189
7 votes
0 answers
466 views

Kähler quotients of affine varieties and GIT

Let $X\subseteq \Bbb C^n$ be a smooth affine variety and $G=K_{\Bbb C}$ a complex reductive group acting linearly on $\Bbb C^n$ preserving $X$ (where $K$ is a maximal compact subgroup of $G$). Suppose ...
SHP's user avatar
  • 779
-1 votes
1 answer
172 views

Tensor bundles as G structures [closed]

For a smooth, real surface $\Sigma$, its bundle of symmetric, bi-linear forms $S^2T\Sigma$ reduced to a $PGL(2,\mathbb{R})$ structure. A similar reduction(with different structure group) can be done ...
Mike Cocos's user avatar
5 votes
2 answers
1k views

A question about Marsden-Weinstein reduction theory

Let $G$ be a compact Lie group and $\frak g$ be its Lie algebra. Then by Marsden-Weinstein reduction theory we know that if we take $M=T^*G$ and $J \colon M\to \frak g^*$ be its moment map then the ...
user avatar
3 votes
2 answers
380 views

degrees of the invariants for the action of $SL(V)$ on $\wedge^4V$

How can we find the degrees of the invariants for the action of $SL(V)$ on $\wedge^4V$ , $dimV=8$ by the model in the Lie algebra $E_7$.
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