Discontinuous groups in positive characteristic and automorphisms of Mumford curves

@article{Cornelissen1999DiscontinuousGI,
  title={Discontinuous groups in positive characteristic and automorphisms of Mumford curves},
  author={Gunther Cornelissen and Fumiharu Kato and Aristeides Kontogeorgis},
  journal={Mathematische Annalen},
  year={1999},
  volume={320},
  pages={55-85}
}
A Mumford curve of genus g (>1) over a non-archimedean valued field k of positive characteristic has at most max{12(g-1), 2 g^(1/2) (g^(1/2)+1)^2} automorphisms. This bound is sharp in the sense that there exist Mumford curves of arbitrary high genus that attain it (they are fibre products of suitable Artin-Schreier curves). The proof provides (via its action on the Bruhat-Tits tree) a classification of discontinuous subgroups of PGL(2,k) that are normalizers of Schottky groups of Mumford… 
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1. The present paper continues the investigation begun in (5). This earlier paper concluded with the description of a pencil P of canonical curves of genus 6 on a del Pezzo quintic surface F, but had…