Geoffrey Smith : Kernel bundles on projective space

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

At

Oct. 17, 2022, 3 p.m.

In

636 SEO

Abstract

While vector bundles on $\mathbb{P}^2$ are well-studied, much less is known about vector bundles on higher-dimensional projective spaces. In this talk, I will partially address this problem by discussing properties of vector bundles on projective space that can be described as the kernel of a general map between relatively simple bundles (e.g., direct sums of line bundles and (co)tangent bundles). More precisely, I will describe circumstances under which these bundles have cohomology that is as simple as possible, are stable, and are ample. This talk is based on joint work with Izzet Coskun and Jack Huizenga.