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

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 the obstructions are nontrivial, we obtain some partial results for generic vanishing of Koszul cohomology groups.

25 pages, to appear in Pacific J. Math

References in corpus (2)

• Green's Conjecture for curves on arbitrary K3 surfaces
• On the Maximal Rank Conjecture for Line Bundles of Extremal Degree

Cited by in corpus (2)

• Tropical independence II: The maximal rank conjecture for quadrics
• Embeddings of general curves in projective spaces: the range of the quadrics