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. A...

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Published in:arXiv.org 2005-04
Main Authors: Behrend, K, Noohi, B
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Language:English
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Automorphisms
Classification
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description 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.
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subjects Automorphisms
Classification
title Uniformization of Deligne-Mumford curves
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