Inductive characterizations of hyperquadrics

We give two characterizations of hyperquadrics: one as non-degenerate smooth projective varieties swept out by large dimensional quadric subvarieties passing through a point; the other as $LQEL$-manifolds with large secant defects

Symplectic Resolutions for Coverings of Nilpotent Orbits

Let \0 be a nilpotent orbit in a semisimple complex Lie algebra \g. Denote by $G$ the simply connected Lie group with Lie algebra \g. For a $G$-homogeneous covering M \to \0, let $X$ be the normalization of \bar{\0} in the function field of $M$. In this note, we study the existence of symplectic resolutions for such coverings $X$

Symplectic resolutions for nilpotent orbits (II)

We prove that for any two projective symplectic resolutions $Z_1$ and $Z_2$ for a nilpotent orbit closure in a complex simple Lie algebra of classical type, then $Z_1$ is deformation equivalen to $Z_2$.Comment: An error is corrected, and the affirmation is weakene

A survey on symplectic singularities and resolutions

This is a survey written in an expositional style on the topic of symplectic singularities and symplectic resolutions, which could also serve as an introduction to this subject

Mukai flops and deformations of symplectic resolutions

We prove that two projective symplectic resolutions of \cit^{2n}/G are connected by Mukai flops in codimension 2 for a finite sub-group G < \Sp(2n). It is also shown that two projective symplectic resolutions of \cit^4/G are deformation equivalent