Moduli spaces of framed instanton bundles on CP^3 and twistor sections of moduli spaces of instantons on C^2

TL;DR

This paper establishes an isomorphism between the moduli space of certain holomorphic bundles on CP^3 and a subvariety in the twistor space of instanton moduli, revealing geometric structures and holonomy properties.

Contribution

It introduces a novel isomorphism linking moduli spaces of bundles on CP^3 to twistor sections, and analyzes the geometric and holonomy properties of these spaces.

Findings

Isomorphism between moduli space of bundles on CP^3 and twistor subvariety

Identification of a torsion-free affine connection with holonomy in Sp(2n,C)

Characterization of the moduli space as a complex manifold

Abstract

We show that the moduli space $M$ of holomorphic vector bundles on $CP^3$ that are trivial along a line is isomorphic (as a complex manifold) to a subvariety in the moduli of rational curves of the twistor space of the moduli space of framed instantons on $\R^4$, called the space of twistor sections. We then use this characterization to prove that $M$ is equipped with a torsion-free affine connection with holonomy in $Sp(2n,\C)$.