Stability of special generalized null correlation bundles on $\mathbb{P}^{5}$

TL;DR

This paper investigates the stability and moduli space structure of special generalized null correlation bundles on , establishing their stability under certain conditions and revealing the complexity of the moduli space with potentially many irreducible components.

Contribution

It proves the stability of special generalized null correlation bundles on  and shows that their moduli space components can be arbitrarily numerous.

Findings

Special generalized null correlation bundles are stable under certain numerical conditions.

The closure of the subvariety parametrizing these bundles forms an irreducible component of the moduli space.

The number of irreducible components of the moduli space can be arbitrarily high.

Abstract

In this paper, we study special generalized null correlation bundles on $\mathbb{P}^{5}$. We prove that special generalized null correlation bundles on $\mathbb{P}^{5}$ are stable under some numerical conditions. Moreover, we prove that the closure of the subvariety parametrizing stable special generalized null correlation bundles is an irreducible component of the moduli space of rank $4$ stable vector bundles with corresponding Chern classes on $\mathbb{P}^{5}$. As an application, we prove that the number of irreducible components of moduli space of rank $4$ stable vector bundles on $\mathbb{P}^5$ with some fixed Chern classes can be arbitrarily high.