A splitting criterion for rank 2 vector bundles on hypersurfaces in P^4

TL;DR

This paper extends Horrocks' splitting criterion for rank two vector bundles from P^3 to certain hypersurfaces in P^4, under specific Chern class conditions, and explores other splitting criteria.

Contribution

It generalizes Horrocks' criterion to hypersurfaces in P^4 with assumptions on Chern classes, advancing the understanding of vector bundle splitting conditions.

Findings

Horrocks' criterion extended to hypersurfaces in P^4

Conditions on Chern classes are crucial for splitting

Other splitting criteria are also analyzed

Abstract

We show that Horrocks' criterion for the splitting of rank two vector bundles in P^3 can be extended, with some assumptions on the Chern classes, on non singular hypersurfaces in P^4. Extension of other splitting criterion are studied.