The moment-map tag has no wiki summary.

**0**

votes

**0**answers

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**

votes

**2**answers

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**

votes

**3**answers

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

**0**answers

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 ...