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0
votes
0answers
24 views

Momentum map for $U(n)$ acting on $\mathbb{C}^{n}$ $J(z)=-\mbox{Im}<\xi z,w>$

I think the momentum map is $J(z)=-\mbox{Im}<\xi z,w>$? is all right? to verify this I have to do that: $$i_{\xi_{M}}\omega=dH_{\xi}$$ where with $\xi_{M}z=\xi z$ I noted infinitesimal action. ...
12
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2answers
1k views

What is the significance that the Springer resolution is a moment map?

Let $\mathcal{B}$ be the flag variety and $\mathcal{N} \subset \mathfrak{g}$ is the nilpotent cone. We know that the Springer resolution $$ \mu: T^*\mathcal{B}\rightarrow \mathcal{N} $$ is the moment ...
4
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3answers
623 views

Why can we define the moment map in this way (i.e. why is this form exact)?

Given a symplectic manifold $(X, \omega)$ and a group $G$ acting on $X$ preserving the symplectic form, we define the moment map $\mu : X \to \mathfrak{g}^*$ so that $$ \langle d\mu(v), \xi\rangle = ...
2
votes
0answers
257 views

Are schematic fixed points of a torus action on an affinized twistor deformation flat?

This is a follow-up to some earlier questions about flatness of schematic fixed points of certain deformations. Since I could never come up with good enough hypotheses in those examples, let me try a ...