On the rationality of the moduli space of instanton bundles on the projective 3-space

TL;DR

This paper proves that the moduli space of certain instanton bundles on projective 3-space is rational and irreducible, extending known results to bundles of arbitrary rank and confirming longstanding conjectures.

Contribution

It establishes the rationality and irreducibility of the moduli space of endomorphism-general instanton bundles of any rank on projective space, including rank-two instantons.

Findings

Proves the rationality of the moduli space for arbitrary rank instanton bundles.

Confirms the irreducibility of the moduli space.

Extends classical results to higher-rank instanton bundles.

Abstract

We prove the rationality and irreducibility of the moduli space of---what we call---the endomorphism-general instanton vector bundles of arbitrary rank on the projective space. In particular, we deduce the rationality of the moduli spaces of rank-two mathematical instantons. This problem was first studied by Hartshorne, Hirschowitz-Narasimhan in the late 1970s, and it has been reiterated within the framework of the ICM 2018.