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Boundary of Hurwitz Spaces and Explicit Patching

✍ Scribed by Jean-Marc Couveignes

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
425 KB
Volume
30
Category
Article
ISSN
0747-7171

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✦ Synopsis

We describe a general method for the study and computation of Hurwitz spaces of curves of any genus. It is based on a careful combinatorial study of the associated Jacobian.

The key tool is an adapted cell decomposition of the cohomology of a graph (used here for the intersection graphs of special curves). We illustrate this method in the context of modular curves to produce modular units. We also give a detailed simple example and show how the algebraic difficulty of Hurwitz spaces computation can be reduced to its minimum.

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