Independent parameters for special instanton bundles on P2n+1P2n+1

Motivated by Yang–Mills theory in 4n4n dimensions, and generalizing the notion due to Atiyah, Drinfeld, Hitchin and Manin for n=1n=1, Okonek, Spindler and Trautmann introduced instanton bundles and special instanton bundles as certain algebraic vector bundles of rank 2n2n on the complex projective space P2n+1P2n+1. The moduli space of special instanton bundles is shown to be rational.

► Instanton bundles are certain algebraic vector bundles of rank 2n on P2n+1P2n+1. ► Their study has been motivated by Yang–Mills theory in 4n dimensions. ► Spindler and Trautmann have introduced moduli spaces of special instanton bundles. ► These spaces are shown to be rational, even if Poincaré families do not exist. ► The proof involves a case of Noether’s problem, and Severi–Brauer varieties.