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Given a finite unbranched covering of a nonsingular projective scheme weanalyse the morphism between moduli spaces of sheaves induced by pullback. Wehave a closer look at cyclic coverings and, in particular, at canonicalcoverings of surfaces. Our main application is the construction of Lagrangiansubvarieties of certain irreducible holomorphically symplectic manifolds thatarise from moduli spaces of sheaves on K3 or abelian surfaces.

Subvarieties of moduli spaces of sheaves via finite coverings