## Generic vanishing and the birational geometry of irregular varieties

### Lecture 1Christopher HACON

Course Description
In these lectures we will survey the generic vanishing results of Green, Lazarfeld, Hacon, Popa, Pareschi and others and discuss their applications to the study of the birational geometry of irregular varieties i.e. smooth projective varieties such that $$H^0(\Omega^1_X) \neq 0$$. In particular we will discuss results concerning the cohomological characterization of abelian varieties, the singularities of divisors on abelian varieties, the pluricanonical maps of irregular varieties and a recent result of Cao-Paun which proves the Iitaka conjecture for fiber spaces $$f:X \to Y$$ where $$Y$$ is a variety of maximal Albanese dimension (eg. an abelian variety).

### 講義詳細

2016年度・前期集中

2016年6月17日 から 7月01日

Christopher HACON（Distinguished Visiting Professor, Kyoto University / Distinguished Professor, University of Utah）

Room 127, Graduate School of Science Bldg No 3