Izzet Coskun : Rational curves on varieties

Posted by Alina Carmen Cojocaru , part of the Number Theory Seminar.

At

Oct. 29, 2008, 2 p.m.

In

SEO 636

Abstract

Conjecturally there is a very close connection between the existence of rational points on a variety X and the existence of rational curves and abelian subvarieties on X. In this talk, I will discuss some geometric conditions, such as rationality, unirationality and rational connectedness, that guarantee that X has many rational curves. I will explain some results and questions about rational curves on hypersurfaces and their implications for existence of points over function fields of curves.