SYMPLECTIC INSTANTON BUNDLES ON P3 AND ’T HOOFT INSTANTONS

Abstract. We study the moduli space In,r of rank-2r symplectic instanton vector bun-dles on P3 with r ≥ 2 and second Chern class n ≥ r + 1, n − r ≡ 1(mod2). We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus I∗n,r of tame symplectic instantons is irreducible and has the expected dimension, equal to 4n(r + 1) − r(2r + 1). The proof is inherently based on a relation between the spaces I∗n,r and the moduli spaces of ’t Hooft instantons. 1