# Generic vanishing and the birational geometry of irregular varieties

2016/06/17 Fri 14:00 - 16:30
2016/06/22 Wed 10:00 - 12:00
2016/06/24 Fri 14:00 - 16:30
2016/06/29 Wed 10:00 - 12:00
2016/07/01 Fri 14:00 - 16:30

3号館127大会議室

Christopher Hacon

Kyoto University / University of Utah

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 $H^0(\Omega ^1_X) ¥ne 0$. 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).

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