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 $ {P}^{2n+1}$ with $ n\ge 2$ . The investigation of '\''t Hooft instanton bundles that were introduced by Ottaviani is continued. Furthermore, the concept of Rao--Skiti instanton bundles is considered. On $ {P}^3$ , such instanton bundles were studied independently by Rao and Skiti, but for higher odd-dimensional projective spaces these objects are new. The main results of the article concern the rationality of the moduli spaces of '\''t Hooft and Rao--Skiti instanton bundles, respectively, and the reducibility of the moduli space of symplectic instanton bundles.