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

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

Perchlorate environmental occurrences, health effects, and remediation technologies

Perchlorate is a widespread pollutant in the environment. It can be produced naturally by atmospheric photochemical reactions or synthesized in large quantities for industrial, military, and pyrotechnic applications. Perchlorate can affect human thyroid function by interfering with iodide uptake and thus has significant public health ramifications. This presentation will provide the current state of science and technology with respect to the source and occurrence of perchlorate in natural environments, its risk assessment, and recent advances in treatment technologies to remove perchlorate from contaminated water. Although perchlorate is a powerful oxidant, it is highly soluble and stable in water and soil and can thus persist in the environment. The discussion will focus on various treatment technologies such as selective ion exchange, reverse osmosis, and biological reduction which can be used to remove perchlorate from contaminated water and thus to minimize its health risks to the public.peer-reviewe

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