Online Talk

*Please note the change in time*

Zoom link:  https://princeton.zoom.us/j/91248028438

Passcode required

Projective spaces are the only smooth projective varieties with ample (locally free) tangent sheaf. This statement was originally known as Hartshorne's conjecture and proved by Mori in his seminal paper "Projective manifolds with ample tangent bundles." On the other hand, by the jacobian criterion, a d-dimensional variety is smooth iff its tangent sheaf is locally free of rank d. In positive characteristic p>0, the jacobian criterion has a Frobenius-theoretic analog, namely Kunz's theorem: a d-dimensional variety is smooth iff the kernel of its Frobenius-trace morphism is locally free of rank p^d-1. It is then natural to ask for a Frobenius-theoretic analog of Mori--Hartshorne's characterization of projective spaces among smooth projective varieties. That is, are projective spaces in positive characteristics the only smooth projective varieties with ample Frobenius-trace kernel? I'll discuss answers to this question in my talk.

This is joint work with Zsolt Patakfalvi (EPFL).