Framed symplectic sheaves on surfaces

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A framed symplectic sheaf on a smooth projective surface X is a torsion-free sheaf E together with a trivialization on a divisor D X and a morphism Λ²Eₓ satisfying some additional conditions. We construct a moduli space for framed symplectic sheaves on a surface, and present a detailed study for X=PC². 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.