Some results on the generic vanishing of Koszul cohomology via deformation theory
Abstract
We study the deformation-obstruction theory of Koszul cohomology groups of grd'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.
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