## EVENT DETAILS AND ABSTRACT

**Algebraic Geometry Seminar**
**Title:** Characterization of abelian varieties for log pairs

**Speaker:** Yuan Wang

**Speaker Info:** Northwestern

**Brief Description:**

**Special Note**:

**Abstract:**

Let $X$ be a projective variety. A celebrated theorem of Kawamata says that if $X$ is smooth and $\kappa(X)=0$, then the Albanese morphism of $X$ is an algebraic fiber space. Thus $\kappa(X)=0$ and $\dim X$ being equal to the dimension of ${\rm Alb}(X)$, the Albanese variety of $X$, implies that $X$ is birational to an abelian variety. Later it was shown by Chen and Hacon that if $\dim X=\dim({\rm Alb}(X))$, then as long as one of $h^0(X,\omega_X^{\otimes m})$, the plurigenera of $X$, is $1$ for some $m\ge 2$, $X$ is birational to an abelian variety. In this talk I will discuss the case where $X$ is not necessarily smooth. I consider a pair $(X,\Delta)$ with reasonable singularities and found out that in this case, the Kodaira dimension and the log plurigenera of $(X,\Delta)$, and the dimension of Albanese variety of $X$ can still characterize abelian varieties up to birational equivalence. In particular, in this talk I will present a result that generalizes Kawamata's result to log canonical pairs and another one that generalizes the result of Chen and Hacon to klt pairs.

**Date:** Thursday, October 19, 2017

**Time:** 4:00pm

**Where:** Lunt 107

**Contact Person:** Mihnea Popa

**Contact email:** mpopa@math.northwestern.edu

**Contact Phone:**

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