Veech holomorphic families of Riemann surfaces, holomorphic sections, and Diophantine problems
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Abstract:
In this paper, we construct holomorphic families of Riemann surfaces from Veech groups and characterize their holomorphic sections by some points of corresponding flat surfaces. The construction gives us concrete solutions for some Diophantine equations over function fields. Moreover, we give upper bounds of the number of holomorphic sections of certain holomorphic families of Riemann surfaces.References
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Additional Information
- Yoshihiko Shinomiya
- Affiliation: Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo 152-8551, Japan
- MR Author ID: 975740
- Email: shinomiya.y.aa@m.titech.ac.jp
- Received by editor(s): April 10, 2012
- Received by editor(s) in revised form: October 25, 2012
- Published electronically: January 21, 2014
- © Copyright 2014
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 366 (2014), 3161-3190
- MSC (2010): Primary 30F60; Secondary 32G15
- DOI: https://doi.org/10.1090/S0002-9947-2014-06056-X
- MathSciNet review: 3180743