Lei Song : A generalization of Kempf's singularity theorem

Posted by Lei Song , part of the Graduate Student Colloquium.

At

Oct. 7, 2013, 5:30 p.m.

In

SEO 636

Abstract

Given a smooth complex projective variety $X$, the line bundles on X having nontrivial sections form a closed subset $W^0(X)$ of the Picard scheme of X. I will show that if every divisor $D$ in a fixed linear system $|L|$ is semi-regular, then there exists a Zariski open neighborhood of $L$ on $W^0(X)$ which has at worst rational singularities. This generalizes Kempf's result for curves.