Rational families of instanton bundles on ℙ2n+1

Abstract

This paper is devoted to the theory of symplectic instanton bundles on an odd dimensional projective space P 2n+1 with n > 2. We study the ’t Hooft instanton bundles introduced by Ottaviani and a new family of instanton bundles which generalizes one introduced on P 3 independently by Rao and Skiti. The main result is the determination of the birational types of the moduli spaces of ’t Hooft and of Rao{Skiti instanton bundles, respectively. Assuming a conjecture of Ottaviani, we show that the moduli space of all symplectic instanton bundles on P 2n+1 with n > 2 is reducible.