Some results on the generic vanishing of Koszul cohomology via deformation theory

Jie Wang

Vol. 273 (2015), No. 1, 47–73

DOI: 10.2140/pjm.2015.273.47

Abstract

We study the deformation-obstruction theory of Koszul cohomology groups of $g_d^r$’s on singular nodal curves. We compute the obstruction classes for Koszul cohomology classes on singular curves to deform to a smooth one. In the case where the obstructions are nontrivial, we obtain some partial results for generic vanishing of Koszul cohomology groups.

Keywords

Koszul cohomology, general curves, deformation theory, generic vanishing, maximal rank conjecture

Mathematical Subject Classification 2010

Primary: 14H51

Milestones

Received: 6 June 2013

Revised: 14 April 2014

Accepted: 25 April 2014

Published: 6 December 2014