A framed symplectic sheaf on a smooth projective surface $X$ is a torsion-free sheaf $E$ together with a trivialization on a divisor $D\subseteq X$ and a morphism $\Lambda^{ 2}E\rightarrow\mathcal{ O}_{ X}$ 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.
Categories: math.AG