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 subset of X and a morphism Lambda E-2 -> OX satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for X = P-C(2). In this case, the moduli space is irreducible and admits an ADHM-type description and a birational proper map onto the space of framed symplectic ideal instantons.