## Generic vanishing and the birational geometry of irregular varieties

###
**Lecture 1**
Christopher 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).

### Details

- Year/Term
- 2016 / Intensive, First semester

- Date
- June 17th to July 1st, 2016

- Faculty/

Graduate School - Graduate School of Science

- Language
- English

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

- Place
- Room 127, Graduate School of Science Bldg No 3

### Related Courses

**Top Global Course Special Lectures 1 “Loop space decompositions in homotopy theory with applications to Poincaré Duality spaces”**

Stephen Theriault

Graduate School of Science

2021**Vertex algebras, instanton counting and invariants of 3 and 4 dimensional manifolds**

Boris FEIGIN

Graduate School of Science

2019**Top Global Course Special Lectures “K-theory of group C∗-algebras and applications”**

Gennadi Kasparov

Graduate School of Science

2019**Top Global Course Special Lectures “Integral equations, the spectral theorem and an introduction to noncommutative geometry”**

Nigel Higson

Graduate School of Science

2019