2021-03-192021-03-192017-07-03Castaño Domínguez, A. (2017). Exponents of Some One-Dimensional Gauss–Manin Systems. Publications of the Research Institute for Mathematical Sciences (PRIMS), 53 (3), 431-455.1663-4926https://hdl.handle.net/11441/106351In 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.application/pdfengAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Exponents of a D-module, Gauss–Manin system, hypergeometric integralinfo:eu-repo/semantics/articleinfo:eu-repo/semantics/openAccess10.4171/PRIMS/53-3-5