Moduli of mathematical instanton vector bundles with odd c_2 on projective space

TL;DR

This paper proves that the moduli space of rank-2 mathematical instanton vector bundles with odd second Chern class n on projective 3-space is irreducible for all odd n, extending previous results for small n.

Contribution

It establishes the irreducibility of the moduli space I_n for all odd n, a significant generalization beyond known cases for small n.

Findings

Irreducibility of I_n proven for all odd n.

Extends previous results limited to small n.

Provides new insights into the structure of instanton moduli spaces.

Abstract

The problem of irreducibility of the moduli space I_n of rank-2 mathematical instanton vector bundles with arbitrary positive second Chern class n on the projective 3-space is considered. The irreducibility of I_n was known for small values of n: Barth 1977 (n=1), Hartshorne 1978 (n=2), Ellingsrud and Stromme 1981 (n=3), Barth 1981 (n=4), Coanda, Tikhomirov and Trautmann 2003 (n=5). In this paper we prove the irreducibility of I_n for an arbitrary odd n.