Exponents of some one-dimensional Gauss-Manin cohomologies
arXiv:1504.08214 · doi:10.4171/prims/53-3-5
Abstract
In this paper we provide a purely algebraic characterization of the exponents of one-dimensional direct images of a structure sheaf by a rational function, related to the vanishing of the cohomologies of a certain Koszul complex associated with such a morphism. This can be extended to a more general family of Gauss-Manin systems. As an application, we calculate a set of possible exponents of the Gauss-Manin cohomology of some arrangements of hyperplanes with multiplicities, relevant to Dwork families and mirror symmetry.
arXiv comment18 pages, final version