Rational families of instanton bundles on P²ⁿ⁺¹

2012/04/23 by Costa, L., Hoffmann, N., Miró-Roig, R. M. +1
#14D21 (Primary) 14D20 #14J60 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1204.5077

Abstract

This paper is devoted to the theory of symplectic instanton bundles on an odd dimensional projective space \mathbb P²ⁿ⁺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 \mathbb P³ 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 P²ⁿ⁺¹ with n≥ 2 is reducible.

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