Birational geometry of higher-dimensional algebraic varieties higher-dimensional algebraic

我主要学习高维代数变种的二分几何。我利用混合霍奇结构理论得到了各种消失定理。通过这些新的消失定理，我建立了对数正则对最小模型理论的基本定理。我还研究了丰度猜想，孤立对数正则奇点，混合霍奇结构的变化，等等。除了上述研究之外，我还对环几何、奇异代数曲面、Kodaira正则束公式的推广等方面感兴趣。

I mainly studied the birational geometry of higher-dimensional algebraic varieties. I obtained various vanishing theorems by using the theory of mixed Hodge structures. By these new vanishing theorems, I established the fundamental theorems of the minimal model theory for log canonical pairs. I also studied the abundance conjecture, isolated log canonical singularities, variations of mixed Hodge structure, and so on. In addition to the above mentioned studies, I am interested in the toric geometry, singular algebraic surfaces, generalizations of Kodaira's canonical bundle formula, and so on.