Analytic Moduli Spaces of Simple (Co)Framed Sheaves

Abstract

Abstract. Let X be a complex space and F a coherent O X -module. A F -(co)framed sheaf on X is a pair (E, ϕ) with a coherent O X -module E and a morphism of coherent sheaves ϕ : F −→ E (resp. ϕ : E −→ F ). Two such pairs (E, ϕ) and (E ′ , ϕ ′ ) are said to be isomorphic if there exists an isomorphism of sheaves α : E −→ E ′ with α • ϕ = ϕ ′ (resp. ϕ ′ • α = ϕ). A pair (E, ϕ) is called simple if its only automorphism is the identity on E. In this note we prove a representability theorem in a relative framework, which implies in particular that there is a moduli space of simple F -(co)framed sheaves on a given compact complex space X.