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

我主要研究高维代数簇的双有理几何。利用混合Hodge结构的理论，得到了各种消失定理。利用这些新的消失定理，建立了对数典型偶极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Hodge结构的变化等，除此之外，我还对复曲面几何、奇异代数曲面、科代拉正则丛公式的推广等感兴趣。

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.