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

Abstract

Symplectic instanton vector bundles on the projective space ${\mathbb{P}}^3$ constitute 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 $r\ge 2$ and second Chern class $n\ge r,n\equiv r(\mathrm{mod}2)$. We give an explicit construction of an irreducible component $I_{n,r}^{\ast }$ of this space for each such value of $n$ and show that $I_{n,r}^{\ast }$ has the expected dimension $4n(r+1)-r(2r+1)$.

14 pages

References in corpus (1)

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