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Moscow Mathematical Journal, 2022, Volume 22, Number 1, Pages 133–168
DOI: https://doi.org/10.17323/1609-4514-2022-22-1-133-168
(Mi mmj820)
 

Period integrals associated to an affine Delsarte type hypersurface

Susumu Tanabé

Department of Mathematics, Galatasaray University, Çırağan cad. 36, Beşiktaş, Istanbul, 34357, Turkey
References:
Abstract: We calculate the period integrals for a special class of affine hypersurfaces (deformed Delsarte hypersurfaces) in an algebraic torus by the aid of their Mellin transforms. A description of the relation between poles of Mellin transforms of period integrals and the mixed Hodge structure of the cohomology of the hypersurface is given. By interpreting the period integrals as solutions to Pochhammer hypergeometric differential equation, we calculate concretely the irreducible monodromy group of period integrals that correspond to the compactification of the affine hypersurface in a complete simplicial toric variety. As an application of the equivalence between oscillating integral for Delsarte polynomial and quantum cohomology of a weighted projective space $\mathbb{P}_{\mathbf{B}}$, we establish an equality between its Stokes matrix and the Gram matrix of the full exceptional collection on $\mathbb{P}_{\mathbf{B}}$.
Key words and phrases: affine hypersurface, Hodge structure, hypergeometric function.
Bibliographic databases:
Document Type: Article
MSC: Primary 14M99; Secondary 32S25, 32S40
Language: English
Citation: Susumu Tanabé, “Period integrals associated to an affine Delsarte type hypersurface”, Mosc. Math. J., 22:1 (2022), 133–168
Citation in format AMSBIB
\Bibitem{Tan22}
\by Susumu~Tanab\'e
\paper Period integrals associated to an affine Delsarte type hypersurface
\jour Mosc. Math.~J.
\yr 2022
\vol 22
\issue 1
\pages 133--168
\mathnet{http://mi.mathnet.ru/mmj820}
\crossref{https://doi.org/10.17323/1609-4514-2022-22-1-133-168}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129143648}
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