Classification of monads and a new moduli component of stable rank 2 bundles on $\mathbb{P}^3$ with even determinant and $c_2=9$

TL;DR

This paper classifies minimal monads for stable rank 2 bundles on projective 3-space with specific Chern classes, extending previous work and discovering a new moduli space component.

Contribution

It extends the classification of minimal monads for stable rank 2 bundles on P^3 with c_2=9 and proves the existence of a new moduli component.

Findings

Extended classification of minimal monads to c_2=9

Identified a new component in the moduli space B(9)

Partial classification with two exceptions

Abstract

The goal of this paper is to classify all minimal monads whose cohomology is a stable rank 2 bundle on $\mathbb{P}^3$ with Chern classes $c_1=0$ and $c_2=9$, with possible exception of two non-negative minimal monads, and thus we extend the classification of the minimal monads made by Hartshorne and Rao in \cite[Section 5.3]{HR91} when $c_2\leq8$. We also prove the existence of a new component of the moduli space $\mathcal{B}(9)$ which is distinct from the Hartshorne and Ein components.