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SIGMA, 2017, Volume 13, 030, 32 pages (Mi sigma1230)  

GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities

Jie Zhou

Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada

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.

Keywords: GKZ system; chain integral; orbifold singularity; Hesse pencil.

Funding Agency
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.


DOI: https://doi.org/10.3842/SIGMA.2017.030

Full text: PDF file (613 kB)
Full text: http://www.emis.de/.../030
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Bibliographic databases:

ArXiv: 1606.08352
MSC: 14J33; 14Q05; 30F30; 34M35
Received: October 1, 2016; in final form May 14, 2017; Published online May 20, 2017
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Citation: Jie Zhou, “GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities”, SIGMA, 13 (2017), 030, 32 pp.

Citation in format AMSBIB
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\yr 2017
\vol 13
\papernumber 030
\totalpages 32
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