Independent parameters for special instanton bundles on P^{2n+1}

TL;DR

This paper studies special instanton bundles on complex projective spaces, proving their moduli space is rational, and extends classical instanton theory to higher dimensions motivated by Yang-Mills theory.

Contribution

It introduces and analyzes special instanton bundles on P^{2n+1}, demonstrating the rationality of their moduli space, generalizing previous instanton concepts.

Findings

Moduli space of special instanton bundles is rational.

Generalization of instanton bundles to higher dimensions.

Connection to Yang-Mills theory in 4n dimensions.

Abstract

Motivated by Yang-Mills theory in 4n dimensions, and generalizing the notion due to Atiyah, Drinfeld, Hitchin and Manin for n=1, Okonek, Spindler and Trautmann introduced instanton bundles and special instanton bundles as certain algebraic vector bundles of rank 2n on the complex projective space P^{2n+1}. The moduli space of special instanton bundles is shown to be rational.