GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
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...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148596 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862664222115102720 |
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| author | Zhou, J. |
| author_facet | Zhou, J. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-12-07T15:14:12Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148596 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:14:12Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Zhou, J. 2019-02-18T16:26:31Z 2019-02-18T16:26:31Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 14J33; 14Q05; 30F30; 34M35 DOI:10.3842/SIGMA.2017.030 https://nasplib.isofts.kiev.ua/handle/123456789/148596 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities Article published earlier |
| spellingShingle | GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities Zhou, J. |
| title | GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities |
| title_full | GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities |
| title_fullStr | GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities |
| title_full_unstemmed | GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities |
| title_short | GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities |
| title_sort | gkz hypergeometric series for the hesse pencil, chain integrals and orbifold singularities |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148596 |
| work_keys_str_mv | AT zhouj gkzhypergeometricseriesforthehessepencilchainintegralsandorbifoldsingularities |