Seminars｜Fostering top leaders in mathematics -- broadening the core and exploring new ground

Seminar

Language	English
From	2011/06/10 10:30
To	2011/06/10 12:00
Place	Room 152, Building No.3, Faculty of Science, Kyoto University
Seminar Name	Algebra Geometrical Seminar
Title	Kodaira Dimension of Irregular Varieites
Field	Algebra Geometry
Speakers	Jungkai Chen
Affiliation	Taiwan National University / RIMS
Abstract	Let $f:X\to Y$ be an algebraic fiber space with generic geometric fiber $F$ , $\dim X=n$ and $\dim Y=m$ . Then Iitaka's $C_{n,m}$ conjecture states $\kappa (X)\geq \kappa (Y)+\kappa (F).$ In particular, if $X$ is a variety with $\kappa(X)=0$ and $f: X \to Y$ is the Albanese map, then Ueno conjecture that $\kappa(F)=0$ . One can regard Ueno's conjecture an important test case of Iitaka's conjecture in general. These conjectures are of fundamental importance in the classification of higher dimensional complex projective varieties. In a recent joint work with Hacon, we are able to prove Ueno's conjecture and $C_{n,m}$ conjecture holds when $Y$ is of maximal Albanese dimension. In this talk, we will introduce some relative results and briefly sketch the proof.
Link	http://www.math.kyoto-u.ac.jp/~mhyo/agsem/agseminar.html