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Working paper

Moduli of symplectic instanton vector bundles of higher rank on projective space $\mathbb{P^3}$. II.

Tikhomirov A. S., Bruzzo U., Markushevich D.
Symplectic instanton vector bundles on the projective space $\mathbb{P^3}$ are a natural generalization of mathematical instantons of rank 2. We study the moduli space $I_{n,r}$ of rank-$2r$ symplectic instanton vector bundles on $\mathbb{P^3}$ with $r\ge2$ and second Chern class $n\ge r+1,\ n-r \equiv 1(\mod2)$. 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 $4n(r+1)-r(2r+1)$.