On a question of Kollár

A Nadel vanishing theorem for metrics with minimal singularities on big line bundles

The purpose of this paper is to establish a Nadel vanishing theorem for big line bundles with multiplier ideal sheaves of singular metrics admitting an analytic Zariski decomposition (such as, metrics with minimal singularities and Siu's metrics). For this purpose, we apply the theory of harmonic integrals and generalize Enoki's proof of Koll'ar's injectivity theorem. Moreover we investigate the asymptotic behavior of harmonic forms with respect to a family of regularized metrics.

伪有效线丛的消失定理

Vanishing theorems for pseudo-effective line bundles

研究在紧凯勒流形上关于闭正流高阶直像的消失定理，通过数值维数建立一般定理，统一多个重要消失定理。

On a question of Kollár

We show: If a bounded domain in a Stein space covers a compact complex space, it must be smooth. This give a negative answer to a question of Kollár. Furthermore, we deduce some related results.

复代数几何中的不可见奇点

Invisible singularities in complex algebraic geometry

该研究在光滑复射影簇间构造具奇异纤维但拓扑光滑的态射，借此否定了四个代数几何领域的猜想与问题。