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Moscow Mathematical Journal, 2022, Volume 22, Number 1, Pages 103–120
DOI: https://doi.org/10.17323/1609-4514-2022-22-1-103-120
(Mi mmj818)
 

This article is cited in 1 scientific paper (total in 1 paper)

On elliptic modular foliations, II

Hossein Movasati

Instituto de Matemática Pura e Aplicada, IMPA, Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, RJ, Brazil
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Abstract: We give an example of a one-dimensional foliation $\mathcal{F}$ of degree two in a Zariski open set of a four-dimensional weighted projective space which has only an enumerable set of algebraic leaves. These are defined over rational numbers and are isomorphic to modular curves $X_0(d)$, $d\in\mathbb{N}$, minus cusp points. As a by-product we get new models for modular curves for which we slightly modify an argument due to J. V. Pereira and give closed formulas for elements in their defining ideals. The general belief was that such formulas do not exist and the emphasis in the literature has been on introducing faster algorithms to compute equations for small values of $d$.
Key words and phrases: holomorphic foliations, modular forms and curves.
Bibliographic databases:
Document Type: Article
MSC: 32M25, 11F55
Language: English
Citation: Hossein Movasati, “On elliptic modular foliations, II”, Mosc. Math. J., 22:1 (2022), 103–120
Citation in format AMSBIB
\Bibitem{Mov22}
\by Hossein~Movasati
\paper On elliptic modular foliations,~II
\jour Mosc. Math.~J.
\yr 2022
\vol 22
\issue 1
\pages 103--120
\mathnet{http://mi.mathnet.ru/mmj818}
\crossref{https://doi.org/10.17323/1609-4514-2022-22-1-103-120}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4407771}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85129228490}
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  • This publication is cited in the following 1 articles:
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