An analytic construction of degenerating curves over complete local rings

David Mumford

Displaying similar documents to “An analytic construction of degenerating curves over complete local rings”

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Curves with only triple ramification

Stefan Schröer (2003)

Annales de l'Institut Fourier

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We show that the set of smooth curves of genus $g \geq 0$ admitting a branched covering $X \to ℙ^{1}$ with only triple ramification points is of dimension at least $max (2 g - 3, g)$ . In characteristic two, such curves have tame rational functions and an analog of Belyi’s Theorem applies to them.

Families of curves and alterations

A. Johan De Jong (1997)

Annales de l'institut Fourier

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In this article it is shown that any family of curves can be altered into a semi-stable family. This implies that if $S$ is an excellent scheme of dimension at most 2 and $X$ is a separated integral scheme of finite type over $S$ , then $X$ can be altered into a regular scheme. This result is stronger then the results of [ Smoothness, semi-stability and alterations to appear in Publ. Math. IHES]. In addition we deal with situations where a finite group acts.