Moduli of symplectic instanton vector bundles of higher rank on projective space $\mathbb{P}^3$

TL;DR

This paper investigates the moduli space of higher-rank symplectic instanton vector bundles on projective 3-space, providing explicit constructions and confirming the expected dimension of an irreducible component.

Contribution

It constructs explicit irreducible components of the moduli space for higher-rank symplectic instanton bundles and determines their expected dimension.

Findings

Constructed explicit irreducible components of the moduli space.

Proved these components have the expected dimension.

Extended the understanding of symplectic instanton bundles to higher ranks.

Abstract

Symplectic instanton vector bundles on the projective space $\mathbb{P}^3$ constitute a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\mathbb{P}^3$ with $r\ge2$ and second Chern class $n\ge r,\ n\equiv r({\rm mod}2)$. We give an explicit construction of an irreducible component $I^*_{n,r}$ of this space for each such value of $n$ and show that $I^*_{n,r}$ has the expected dimension $4n(r+1)-r(2r+1)$.