You are here: Home :: Area NEM :: Mathematics

Kai Behrend, Behrang Noohi

Uniformization of Deligne-Mumford curves

We compute the fundamental groups of non-singular analytic Deligne-Mumford curves, classify the simply connected ones, and classify analytic Deligne-Mumford curves by their uniformization type. As a result, we find an explicit presentation of an arbitrary Deligne-Mumford curve as a quotient stack. Along the way, we compute the automorphism 2-groups of weighted projective stacks 𝒫(n₁, n₂, … n_r). We also discuss connections with the theory of F-groups, 2-groups, and Bass-Serre theory of graphs of groups.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2006, 10/2006
Pages: 111 - 153

Show full article (external site)

Show all available items of this journal

 

Area NEM