Deformations of morphisms of sheaves

Abstract We analyze infinitesimal deformations of morphisms of locally free sheaves on a smooth projective variety X over an algebraically closed field of characteristic zero. In particular, we describe a differential graded Lie algebra controlling the deformation problem. As an application, we study infinitesimal deformations of the pairs given by a locally free sheaf and a subspace of its sections with a view toward Brill-Noether theory.