On Elliptic Modular Foliations, II

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2018-08-05 DOI:10.17323/1609-4514-2022-22-1-103-120

H. Movasati

引用次数: 1

Abstract

We give an example of a one dimensional foliation 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 X0(d), d ∈ 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 has been 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.

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关于椭圆模叶，II

我们给出了一个例子，在一个只有可枚举代数叶集的四维加权投影空间的Zariski开集中，一个二阶的一维叶理F。这些是在有理数上定义的，同构于模曲线X0（d），d∈N减去尖点。作为副产品，我们得到了模曲线的新模型，我们稍微修改了J.V.Pereira的一个论点，并给出了定义理想中元素的闭合公式。人们普遍认为，这种公式并不存在，文献中的重点是引入更快的算法来计算d的小值方程。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.