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Article

Symplectic instanton bundles on ℙ3 and ’t Hooft instantons

European Journal of Mathematics. 2016. Vol. 2. P. 73-86.
Bruzzo U., Markushevich D., Tikhomirov A. S.

We study the moduli space $I_{n,r}$In,r of rank-2r symplectic instanton vector bundles on $\mathbb{P}^3$ℙ3 with $r\ge 2$r⩾2 and second Chern class $n\ge r+1, n-r\equiv 1(\mathrm{mod} 2)$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 $I_{n,r}^*$I∗n,r of tame symplectic instantons is irreducible and has the expected dimension equal to $4n(r+1)-r(2r+1)$.4n(r+1)−r(2r+1) The proof is inherently based on a relation between the spaces $I_{n,r}^*$I∗n,r and the moduli spaces of ’t Hooft instantons.