Uniformization of Deligne-Mumford curves

By K. Behrend, B. Noohi. 2005

80 citations recorded by the source corpus.

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 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e36bc552dff1acb32e9ff20a693ea928e81a9356

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

On the geometry of Deligne-Mumford stacks (2009, background): “The fact quoted in Step 1 is well known and can be found in [ BN , Prop.”
On the classification of rank-two representations of quasiprojective fundamental groups (2007, background): “In the one-dimensional case, aside from a small number of degenerate situations, an orbicurve has a Galois covering which is a smooth curve (see Lemmas 2.3 and 2.6).”
Foundations of Topological Stacks I (2005, background): “t is a 2-dimensional simply connected manifold. It can be seen that the only possibility is that the universal cover be homeomorphic to R2. More details and more examples of this type can be found in [2]. 19.5. Graphs of groups. In this subsection, we brieﬂy indicate how the theory of graphs of grou”
Higher analytic stacks and GAGA theorems (2014, background): “In the classical sense, complex analytic stacks were considered in [4], and non-archimedean analytic stacks were considered in [49, 47] to the best of our knowledge.”