Linked sheaves of modules

Abstract

We introduce a notion of linkage for sheaves of modules on connected Noetherian schemes, extending classical linkage of modules. Linkage is defined for stable sheaves admitting finite free resolutions via the transpose and syzygy functors. We show that linkedness is a local property and that, on affine schemes, a coherent sheaf is linked if and only if its module of global sections is linked. We further show that linkage is preserved under restriction and, under suitable rank conditions, under gluing over connected schemes. We also obtain criteria for the existence of linked subsheaves when the structure sheaf is not a domain. In the projective setting, we compare invariants of linked sheaves, including graded cohomology modules, Castelnuovo-Mumford regularity, and Hilbert polynomials.