Singularities of the modular curve
Date
2001
Authors
Klyachko, A.
Kara, O.
Editor(s)
Advisor
Supervisor
Co-Advisor
Co-Supervisor
Instructor
Source Title
Finite Fields and Their Applications
Print ISSN
1071-5797
Electronic ISSN
Publisher
Academic Press
Volume
7
Issue
3
Pages
415 - 420
Language
English
Type
Journal Title
Journal ISSN
Volume Title
Series
Abstract
Let X0 (l) be the modular curve, parameterizing cyclic isogenies of degree l, and Z0 (l) be its plane model, given by the classical modular equation 'l (X,>)"0. We prove that all singularities of Z0 (l), except two cusps, are intersections of smooth branches, and evaluate the order of contact of these branches.