Moscow Mathematical Journal
Volume 22, Issue 1, January–March 2022 pp. 133–168.
Period Integrals Associated to an Affine Delsarte Type Hypersurface
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 $\mathbb{P}_{\mathbf{B}}$.
2020 Math. Subj. Class. Primary: 14M99; Secondary: 32S25, 32S40
Authors:
Susumu Tanabé (1)
Author institution:(1) Department of Mathematics,
Galatasaray University,
Çırağan cad. 36,
Beşiktaş, Istanbul, 34357, Turkey
Summary:
Keywords: Affine hypersurface, Hodge structure, hypergeometric function.
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