Moduli spaces of framed instanton bundles on CP^3 and twistor sections of moduli spaces of instantons on C^2

Abstract

We show that the moduli space $M$ of holomorphic vector bundles on $CP^3$ that are trivial along a line is isomorphic (as a complex manifold) to a subvariety in the moduli of rational curves of the twistor space of the moduli space of framed instantons on $\R^4$, called the space of twistor sections. We then use this characterization to prove that $M$ is equipped with a torsion-free affine connection with holonomy in $Sp(2n,\C)$.