Analytic moduli spaces of simple (co)framed sheaves

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,f) with a coherent O_X-module E and a morphism of coherent sheaves f : F -> E (resp. f : E -> F). Two such pairs (E,f) and (E',f') are said to be isomorphic if there exists an isomorphism of sheaves g : E -> E' such that gof = f' (resp. f'og = f). A pair (E,f) 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.