Xudong Zheng : Pathologies on surfaces in characteristic $p$, or how I found someone's paper is wrong

Posted by Xudong Zheng , part of the Graduate Algebraic Geometry Seminar.

At

Sept. 2, 2015, 3 p.m.

In

SEO 712

Abstract

In this talk, I will present some constructions of algebraic surfaces in characteristic $p$ which violate the Kodaira vanishing theorem. These surfaces also provide counterexamples to Fujita's positivity theorem for fibered surfaces. Further pathologies on these examples include the existence of non-closed global differential 1-forms and global vector fields, which are both known to be impossible in characteristic zero. I will survey the comparison of characteristic zero with characteristic $p$, sketch the construction, and mention how I encountered these results by noticing errors in a recent published paper.