Vol. 273, No. 1, 2015

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

Jie Wang

Vol. 273 (2015), No. 1, 47–73
Abstract

We study the deformation-obstruction theory of Koszul cohomology groups of gdr’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
Authors
Jie Wang
Department of Mathematics
University of Georgia
Athens, GA 30602
United States