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In any standard symplectic geometry/topology textbook, the concept of Hamiltonian isotopy was introduced: $(M, \omega)$ is a sympplectic manifold. Given a symplectic isotopy $\phi_t : M \rightarrow M …

Given a closed (possibly singular) projective variety $V$ with a symplectic structure and a torus action, there is a moment map $\mu: V \rightarrow Lie(T)^*$. Note that the dimension of $T$ could be …

We have a flat family of projective varieties with a torus $T$ action, over $\mathbb{A}^1$. How do the moment map images of the fibers change when we pass from the generic fiber to the special fiber …

Given a possibly singular, connected, symplectic algebraic variety with a torus action, every fiber of the moment map admits a torus action. Is each fiber of this moment map connected? Any examples or …

May I ask what are the relations between the geometry and combinatorics near a torus fixed point? Any references? In particular, let $S$ be a scheme that is torus invariant with finitely many zero and …

Let $X$ be a possibly singular projective scheme which admits a torus $T$ action and has finitely many $T$ fixed points and one-dimensional $T-$orbits. There are many such schemes in the Grassmannian/ …