Characterizations of projective space and Seshadri constants in positive characteristic
Takumi Murayama (University of Michigan)
Wednesday, September 13, 2017
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.