Revista Matemática Iberoamericana

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Volume 35, Issue 5, 2019, pp. 1451–1484
DOI: 10.4171/rmi/1088

Published online: 2019-05-31

Dwork families and $\mathcal D$-modules

Alberto Castaño Domínguez[1]

(1) Universidade de Santiago de Compostela, Spain and Technische Universität Chemnitz, Germany

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 $\mathcal D$-modules, especially one-dimensional hypergeometric ones.

Keywords: $\mathcal D$-modules, Gauss–Manin systems, Dwork families, hypergeometric $\mathcal D$-modules

Castaño Domínguez Alberto: Dwork families and $\mathcal D$-modules. Rev. Mat. Iberoam. 35 (2019), 1451-1484. doi: 10.4171/rmi/1088