## Student Algebra & Combinatorics

•  Nick Rekuski, Michigan State
•  Splitting Criteria for Vector Bundles on $\mathbb{P}^n$
•  09/23/2019
•  4:30 PM - 5:30 PM
•  C304 Wells Hall

Grothendieck's Theorem says that any vector bundle on $\mathbb{P}^1$ can be decomposed as a finite sum of line bundles. In this talk, we will discuss a generalization of this theorem: Horrocks Splitting Criterion. This criterion completely describes when a vector bundle on $\mathbb{P}^n$ splits as a sum of line bundles. We will then discuss an open conjecture of Hartshorne. If time permits, we will also consider the similar question of classifying when a vector bundle on $\mathbb{P}^n$ decompose as line bundles and twists of the tangent bundle.

## Contact

Department of Mathematics
Michigan State University