Brody's theorem for Deligne-Mumford analytic stacks

Details Brody's theorem for Deligne-Mumford analytic stacks Brody's theorem for Deligne-Mumford analytic stacks

2012-01-12

arxiv.org/abs/1201.2535v1

Mathematics

Complex Variables

Scientific paper

The classical Brody's theorem asserts the equivalence between two notions of hyperbolicity for compact complex spaces, one named after Kobayashi and one expressed in terms of lack of non constant holomorphic entire functions (compactness is only used to prove the harder implication). We extend this theorem to Deligne-Mumford analytic stacks, by first providing definitions of what we think of Kobayashi and Brody hyperbolicity for such objects and then proving the equivalence of these concepts under an assumption of compactness.

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