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The main result of the present paper is a construction of relative modulispaces of stable sheaves over the stack of quasipolarized projective surfaces.For this, we use the theory of good moduli spaces, whose study was initiated byAlper. As a corollary, we extend the relative Strange Duality morphism to thelocus of quasipolarized K3 surfaces.

Moduli spaces of stable sheaves over quasi-polarized surfaces, and the relative Strange Duality morphism