Abstract:
The GKZ system for the Hesse pencil of elliptic curves has more solutions than the period integrals. In this work we give different realizations and interpretations of the extra solution, in terms of oscillating integral, Eichler integral, chain integral on the elliptic curve, limit of a period of a certain compact Calabi–Yau threefold geometry, etc. We also highlight the role played by the orbifold singularity on the moduli space and its relation to the GKZ system.
This research was supported in part by Perimeter Institute for Theoretical Physics. Research at Perimeter Institute is supported by the Government of Canada through Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Research, Innovation and Science.
Received:October 1, 2016; in final form May 14, 2017; Published online May 20, 2017
\Bibitem{Zho17}
\by Jie~Zhou
\paper GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
\jour SIGMA
\yr 2017
\vol 13
\papernumber 030
\totalpages 32
\mathnet{http://mi.mathnet.ru/sigma1230}
\crossref{https://doi.org/10.3842/SIGMA.2017.030}
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This publication is cited in the following 1 articles:
O. Maria Lecian, “Modular structures and extended-modular-group-structures after hecke pairs”, 32Nd International Colloquium on Group Theoretical Methods in Physics (Group32), Journal of Physics Conference Series, 1194, IOP Publishing Ltd, 2019, 012067
Citation in format AMSBIB
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