- 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.
