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

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Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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dc.contributor.author	Zhou, J.
dc.date.accessioned	2019-02-18T16:26:31Z
dc.date.available	2019-02-18T16:26:31Z
dc.date.issued	2017
dc.identifier.citation	GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities / J. Zhou // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 46 назв. — англ.	uk_UA
dc.identifier.issn	1815-0659
dc.identifier.other	2010 Mathematics Subject Classification: 14J33; 14Q05; 30F30; 34M35
dc.identifier.other	DOI:10.3842/SIGMA.2017.030
dc.identifier.uri	http://dspace.nbuv.gov.ua/handle/123456789/148596
dc.description.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.	uk_UA
dc.description.sponsorship	The author dedicates this article to Professor Noriko Yui on the occasion of her birthday. The author is grateful for her constant encouragement and support, and in particular for many inspiring discussions on geometry and number theory. The author would like to thank Murad Alim, An Huang, Bong Lian and Shing-Tung Yau for discussions on open string mirror symmetry which to a large extent inspired this project. He thanks further Kevin Costello, Shinobu Hosono, Si Li and Zhengyu Zong for their interest and helpful conversations on Landau–Ginzburg models and chain integrals, and Don Zagier for some useful discussions on modular forms back in year 2013. He also thanks the anonymous referees whose suggestions have helped improving the article. 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.	uk_UA
dc.language.iso	en	uk_UA
dc.publisher	Інститут математики НАН України	uk_UA
dc.relation.ispartof	Symmetry, Integrability and Geometry: Methods and Applications
dc.title	GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities	uk_UA
dc.type	Article	uk_UA
dc.status	published earlier	uk_UA