Non-vanishing theorems for rank 2 bundles on P^3: a simple approach without the speciality lemma

TL;DR

This paper presents simplified criteria for determining when rank 2 vector bundles on P^3 split, using basic computations to improve upon existing vanishing conditions without relying on complex traditional tools.

Contribution

It introduces new, simpler vanishing conditions for rank 2 bundles on P^3 that avoid heavy traditional methods, enhancing previous results.

Findings

Improved vanishing conditions for splitting of bundles

Simplified computational approach avoiding heavy tools

Enhanced criteria over existing literature

Abstract

The paper investigates vanishing conditions on the first cohomology module of a normalized rank 2 vector bundle E on P^3 which force E to split, and finds therefore strategic levels of non-vanishing for a non-split bundle. The present conditions improve other conditions known in the literature and are obtained with simple computations on the Euler characteristic function, avoiding the speciality lemma, Barth's restriction theorem, the discriminat property, and other heavy tools.