Uniformization of Deligne-Mumford curves
Abstract
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 $\mathcal{P}(n_1,n_2,...,n_r)$. We also discuss connections with the theory of F-groups, 2-groups, and Bass-Serre theory of graphs of groups.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- April 2005
- DOI:
- 10.48550/arXiv.math/0504309
- arXiv:
- arXiv:math/0504309
- Bibcode:
- 2005math......4309B
- Keywords:
-
- Algebraic Geometry;
- 14A20;
- 14H30;
- 30F10;
- 30F20
- E-Print:
- 39 pages, 2 figures