Framed symplectic sheaves on surfaces

A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D\subseteq X$andamorphism$\Lambda^{2}E\rightarrow$\mathcal{O}$_{X}$ satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for $X={\mathbb{P}}_{\mathbb{C}}^2$. In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map into the space of framed symplectic ideal instantons.