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Zapiski Nauchnykh Seminarov POMI, 2016, Volume 446, Pages 165–181
(Mi znsl6288)
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This article is cited in 2 scientific papers (total in 2 papers)
Abel pairs and modular curves
D. Oganesyan Moscow Lomonosov State University
Abstract:
We consider rational functions on algebraic curves which have a single zero and a single pole. A pair consisting of such a function and a curve is called Abel pair; a special case of an Abel pair is a Belyi pair. In this paper, we study moduli spaces of Abel pairs for curves of genus one. In particular, we compute a number of Belyi pairs over the fields $\mathbb C$ and $\overline{\mathbb F_p}$. This approach could be fruitfully used for the study of Hurwitz spaces and modular curves for fields of finite characteristics.
Key words and phrases:
Belyi pairs, dessins d'enfants, Abel pairs, reduction to positive characteristic, embedded graphs, modular curves, elliptic curves.
Received: 30.04.2016
Citation:
D. Oganesyan, “Abel pairs and modular curves”, Combinatorics and graph theory. Part V, Zap. Nauchn. Sem. POMI, 446, POMI, St. Petersburg, 2016, 165–181; J. Math. Sci. (N. Y.), 226:5 (2017), 655–666
Linking options:
https://www.mathnet.ru/eng/znsl6288 https://www.mathnet.ru/eng/znsl/v446/p165
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Statistics & downloads: |
Abstract page: | 170 | Full-text PDF : | 48 | References: | 38 |
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