On the cohomology of rank two vector bundles on P2 and a theorem of Chiantini and Valabrega

TL;DR

This paper characterizes when rank two vector bundles on P2 split, provides an alternative proof of a known theorem, and classifies bundles with small h1(E(-1)) values.

Contribution

It offers a new proof of Chiantini and Valabrega's theorem and classifies normalized rank two bundles with low h1(E(-1)).

Findings

A normalized rank two bundle splits iff h1(E(-1))=0.

Alternative proof of Chiantini and Valabrega's theorem.

Classification of bundles with h1(E(-1)) <= 4.

Abstract

We show that a normalized rank two vector bundle, E, on P2 splits if and only if h1(E(-1)) = 0. Using this fact we give another proof of a theorem of Chiantini and Valabrega. Finally we describe the normalized bundles with h1(E(-1)) <= 4.