p-Buchsbaum rank 2 bundles on the projective space

TL;DR

This paper investigates the classification of 3-Buchsbaum rank 2 vector bundles on the projective space P3, revealing differences from lower Buchsbaum cases and proposing a new conjecture.

Contribution

It extends the understanding of Buchsbaum bundles by analyzing the 3-Buchsbaum case and proposing a conjecture for their classification.

Findings

Normalized 1-Buchsbaum bundles are nullcorrelation bundles.

Normalized 2-Buchsbaum bundles are instanton bundles of charge 2.

3-Buchsbaum bundles differ from lower cases, leading to a new conjecture.

Abstract

It has been proved by various authors that a normalized, 1-Buchsbaum rank 2 vector bundle on P3 is a nullcorrelation bundle, while a normalized, 2-Buchsbaum rank 2 vector bundle on P3 is an instanton bundle of charge 2. We find that the same is not true for 3-Buchsbaum rank 2 vector bundles on P3, and propose a conjecture regarding the classification of such objects.