Deformations of morphisms of sheaves

Abstract

We analyse 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 pairs given by a locally free sheaf and a subspace of it sections with a view towards Brill-Noether theory.

22 pages, revised version according to referee's comments, accepted for publication in Canadian Journal of Mathematics

References in corpus (3)

• Semicosimplicial DGLAs in deformation theory
• Cohomology jump loci of differential graded Lie algebras
• Differential graded Lie algebras controlling infinitesimal deformations of coherent sheaves