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

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dc.contributor.authorZhou, J.
dc.date.accessioned2019-02-18T16:26:31Z
dc.date.available2019-02-18T16:26:31Z
dc.date.issued2017
dc.description.abstractThe 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.sponsorshipThe 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.identifier.citationGKZ 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.issn1815-0659
dc.identifier.other2010 Mathematics Subject Classification: 14J33; 14Q05; 30F30; 34M35
dc.identifier.otherDOI:10.3842/SIGMA.2017.030
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/148596
dc.language.isoenuk_UA
dc.publisherІнститут математики НАН Україниuk_UA
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlieruk_UA
dc.titleGKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularitiesuk_UA
dc.typeArticleuk_UA

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Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13, випуск за цей рік