The singularities of the moduli schemes of curves
β Scribed by Herbert Popp
- Publisher
- Elsevier Science
- Year
- 1969
- Tongue
- English
- Weight
- 1012 KB
- Volume
- 1
- Category
- Article
- ISSN
- 0022-314X
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π SIMILAR VOLUMES
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
The field of moduli K of a curve X a priori defined over the separable closure K s of K need not be a field of definition. This paper shows that the obstruction is essentially the same as the obstruction to K being a field of definition of the cover X ~ X/Aut(X). Using previous results of Dbbes-Doua