Symplectic instanton bundles on P3 and 't Hooft instantons

Abstract

We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on ${\mathbb{P}}^3$ with $r\ge 2$ and second Chern class $n\ge r+1,n-r\equiv 1(\mathrm{mod}2)$. We introduce the notion of tame symplectic instantons by excluding a kind of pathological monads and show that the locus $I_{n,r}^{\ast }$ 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 $I_{n,r}^{\ast }$ and the moduli spaces of 't Hooft instantons

14 pages

References in corpus (1)

• Moduli of mathematical instanton vector bundles with odd c_2 on projective space