Rational families of instanton bundles on $P^{2n+1}$

Abstract

This paper is devoted to the theory of symplectic instanton bundles on an odd dimensional projective space ${\mathbb{P}}^{2n+1}$ with $n\ge 2$. We study the 't Hooft instanton bundles introduced by Ottaviani and a new family of instanton bundles which generalizes one introduced on ${\mathbb{P}}^3$ 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 ${\mathbb{P}}^{2n+1}$ with $n\ge 2$ is reducible.

37 pages. v2: minor revision. final version, to appear in Algebraic Geometry (new open access journal of the Compositio Foundation)