## Algebra Seminar

# Characterizations of projective space and Seshadri constants in positive characteristic

## Takumi Murayama (University of Michigan)

### Wednesday, September 13, 2017
11:15 am

MONT 113 (Storrs)

Projective spaces are, in some sense, the simplest algebraic varieties. It is therefore useful to know when a given variety is actually projective space. A famous result in this direction is due to Mori, who invented bend and break techniques to show that when a variety has a "positive" tangent bundle, it is in fact projective space. A stronger result is known in characteristic zero, and is due to Cho, Miyaoka, and Shepherd-Barron. We will present some progress toward this stronger result in positive characteristic using Seshadri constants and the Frobenius morphism. The key ingredient is a positive-characteristic proof of Demailly's criterion for separation of higher-order jets by adjoint bundles.