CYCLIC COVERINGS OF THE p-ADIC PROJECTIVE LINE BY MUMFORD CURVES
نویسنده
چکیده
Exact bounds for the positions of the branch points for cyclic coverings of the p-adic projective line by Mumford curves are calculated in two ways. Firstly, by using Fumiharu Kato’s ∗-trees, and secondly by giving explicit matrix representations of the Schottky groups corresponding to the Mumford curves above the projective line through combinatorial group theory.
منابع مشابه
ar X iv : 0 80 6 . 08 36 v 1 [ m at h . A G ] 4 J un 2 00 8 p - ADIC HURWITZ NUMBERS
We introduce stable tropical curves, and use these to count covers of the p-adic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers.
متن کاملar X iv : 0 80 6 . 08 36 v 2 [ m at h . A G ] 4 J un 2 00 8 p - ADIC HURWITZ NUMBERS
We introduce stable tropical curves, and use these to count covers of the p-adic projective line of fixed degree and ramification types by Mumford curves in terms of tropical Hurwitz numbers. Our counts depend on the branch loci of the covers.
متن کاملConstruction of p-adic Hurwitz spaces
Moduli spaces for Galois covers of p-adic Mumford curves by Mumford curves are constructed using Herrlich’s Teichmüller spaces, André’s orbifold fundamental groups, and Kato’s graphs of groups encoding ramification data of charts for Mumford orbifolds.
متن کاملMumford dendrograms and discrete p-adic symmetries
In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to p-adic number fields. As an application , we show how strings over a finite alphabet can be encoded in cyclotomic extensions of Qp and discuss p-adic DNA encoding. The application leads to fast p-adic agglomerative hierarchic algorithms similar to the ones recently used e....
متن کاملTheta constants associated with the cyclic triple coverings of the complex projective line branching at six points ∗
Let ψ be the period map for a family of the cyclic triple coverings of the complex projective line branching at six points. The symmetric group S6 acts on this family and on its image under ψ. In this paper, we give an S6-equivariant expression of ψ −1 in terms of fifteen theta constants.
متن کامل