Back to Algebraic Geometry Seminar: Spring 2021
Algebraic Geometry Seminar
Date: Tuesday, Mar 9, 2021
Time: 3:30PM - 4:30PM
Location: Zoom
3:30 pm
Tatsuro Kawakami
The University of Tokyo
Title |
Bogomolov-Sommese vanishing and liftability for surface pairs in positive characteristic |
Abstract |
Bogomolov-Sommese vanishing asserts that the $i$-th logarithmic reflexive differential form of a log canonical projective pair in characteristic zero does not contain a Weil divisorial sheaf of Iitaka dimension bigger than $i$. In positive characteristic, it is known that the vanishing theorem fails. Indeed, there is a simple normal crossing surface pair $(X, D)$ such that the first logarithmic differential form contains a big line bundle in each characteristic. On the other hand, in these counterexamples, we can see that $K_X+D$ is often big. In this talk, I will discuss Bogomolov-Sommese vanishing theorem for a log canonical surface pair $(X, D)$ such that $K_X+D$ is not pseudo-effective in positive characteristic. I also show an application to liftability of surface pairs. |
Algebraic Geometry