Symplectic instanton bundles on P3 and 't Hooft instantons

TL;DR

This paper investigates the structure and properties of the moduli space of symplectic instanton bundles on projective 3-space, introducing tame instantons and establishing their irreducibility and dimension through relations to 't Hooft instantons.

Contribution

It introduces the concept of tame symplectic instantons and proves their moduli space is irreducible with the expected dimension, linking it to 't Hooft instanton moduli spaces.

Findings

The moduli space of tame symplectic instantons is irreducible.

The dimension of this moduli space matches the expected value.

A relation between tame instantons and 't Hooft instantons is established.

Abstract

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 $n\ge r+1,\ n-r\equiv 1(\mathrm{mod}2)$. We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I^*_{n,r}$ of tame symplectic instantons is irreducible and has the expected dimension, equal to $4n(r+1)-r(2r+1)$. The proof is inherently based on a relation between the spaces $I^*_{n,r}$ and the moduli spaces of 't Hooft instantons