2017/07/12 by Voskuil, Harm H., van der Put, Marius
#14E09 #20E08 #30E06 #Algebraic Geometry (math.AG) #FOS: Mathematics
paper · doi:10.48550/arxiv.1707.03644
A Mumford group is a discontinuous subgroup Γ of PGL(2,K), where K denotes a non archimedean valued field, such that the quotient by Γ is a curve of genus 0. As abstract group Γ is an amalgam of a finite tree of finite groups. For K of positive characteristic the large collection of amalgams having two or three branch points is classified. Using these data Mumford curves with a large group of automorphisms are discovered. A long combinatorial proof, involving the classification of the finite simple groups, is needed for establishing an upper bound for the order of the group of automorphisms of a Mumford curve. Orbifolds in the category of rigid spaces are introduced. For the projective line the relations with Mumford groups and singular stratified bundles are studied. This paper is a sequel to our paper "Discontinuous subgroups of PGL(2,K)" published in Journ. of Alg. (2004). Part of it clarifies, corrects and extends work of G.~Cornelissen, F.~Kato and K.~Kontogeorgis.