New families of rank 2 bundles on projective space

TL;DR

This paper introduces new families of stable rank two vector bundles on projective space, analyzes their geometric properties, and determines the structure of their moduli space.

Contribution

It constructs novel monads for stable rank two bundles and characterizes the irreducibility and smoothness of their moduli space.

Findings

Identifies three irreducible components of the moduli space

Provides geometric descriptions of the new bundle families

Proves irreducibility and smoothness properties of these families

Abstract

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\PP$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. Such facts are used to prove that the moduli space of stable rank two vector bundles of zero first Chern class and second Chern class equal to 5 has exactly three irreducible components.