John Kopper : Ample stable vector bundles on rational surfaces

Posted by Izzet Coskun , part of the Algebraic Geometry Seminar.

At

Oct. 11, 2021, 3 p.m.

In

Zoom

Abstract

Ample bundles are among the most important "positive" vector bundles in algebraic geometry. Unfortunately, they cannot be classified by their Chern classes alone. An approach to this problem was suggested by Le Potier, who asks for a classification of those Chern characters for which there exists a stable ample bundle. When the moduli space of stable bundles is irreducible, this is equivalent to asking for the general stable bundle to be ample. I will discuss some recent progress on this problem for (minimal) rational surfaces. This is joint work with Jack Huizenga.