#### 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 ${g}_{d}^{r}$’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
Primary: 14H51