Dwork families and $\mathcal D$-modules

Alberto Castaño Domínguez

doi:10.4171/rmi/1088

JournalsrmiVol. 35, No. 5pp. 1451–1484

Dwork families and $D$ -modules

Alberto Castaño Domínguez
Universidade de Santiago de Compostela, Spain and Technische Universität Chemnitz, Germany

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Abstract

A Dwork family is a one-parameter monomial deformation of a Fermat hypersurface. In this paper we compute algebraically the invariant part of its Gauss–Manin cohomology under the action of certain subgroup of automorphisms. To achieve that goal we use the algebraic theory of $D$ -modules, especially one-dimensional hypergeometric ones.

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Alberto Castaño Domínguez, Dwork families and $D$ -modules. Rev. Mat. Iberoam. 35 (2019), no. 5, pp. 1451–1484

DOI 10.4171/RMI/1088