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Singularities of the Modular Curve

✍ Scribed by Alexander Klyachko; Orhun Kara

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 280 KB
Volume: 7
Category: Article
ISSN: 1071-5797
DOI: 10.1006/ffta.2001.0319

No coin nor oath required. For personal study only.

✦ Synopsis

Let X (l) be the modular curve, parameterizing cyclic isogenies of degree l, and Z (l) be its plane model, given by the classical modular equation l (X, >)"0. We prove that all singularities of Z (l), except two cusps, are intersections of smooth branches, and evaluate the order of contact of these branches.

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