# New moduli components 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 moduli spaces, and identifies the structure of components for specific Chern classes, advancing understanding of vector bundle moduli.

## Contribution

It constructs new moduli components of stable rank two bundles on projective space and describes their geometric properties and irreducibility.

## Key findings

- New infinite series of rational moduli components with growing second Chern class
- Irreducibility and smoothness of certain moduli families
- Exactly three irreducible rational components for second Chern class 5

## Abstract

We present a new family of monads whose cohomology is a stable rank two vector bundle on $\mathbb{P}^3$. We also study the irreducibility and smoothness together with a geometrical description of some of these families. These facts are used to construct a new infinite series of rational moduli components of stable rank two vector bundles with trivial determinant and growing second Chern class. We also prove that the moduli space of stable rank two vector bundles with trivial determinant and second Chern class equal to 5 has exactly three irreducible rational components.