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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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GKZ Hypergeometric Series for the Hesse Pencil, Chain Integrals and Orbifold Singularities
Інший ID:
2010 Mathematics Subject Classification: 14J33; 14Q05; 30F30; 34M35
DOI:10.3842/SIGMA.2017.030
DOI:10.3842/SIGMA.2017.030
Посилання:
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.
Підтримка:
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.
Дата:
2017
Переглядів:
488
Завантажень:
218
Анотація:
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.
