2018/05/29 by Susumu Tanabé, Susumu Tanabe, Tanabe, Susumu
Mathematics · Physics and Astronomy · #14M109 (primary) #32S25 #32S40 (secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #math.AG #msc:14M109 #msc:32S25 #msc:32S40
paper · pdf · doi:10.48550/arxiv.1805.11708
to appear in Moscow Mathematical Journal. vol.22, No. 1, 2022
openalex publication_date 2018/05/29 · arxiv created 2022/01/26 · arxiv updated 2022/01/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 ℙ\bf B, we establish an equality between its Stokes matrix and the Gram matrix of the full exceptional collection on ℙ\bf B.