Graduate Algebraic Geometry Seminar
Xudong Zheng
UIC
Pathologies on surfaces in characteristic $p$, or how I found someone's paper is wrong
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.
Wednesday September 2, 2015 at 3:00 PM in SEO 712