A brody theorem for orbifolds

Frédéric Campana (1) , Jörg Winkelmann (1)

1 IECN - Institut Élie Cartan de Nancy

We study orbifolds, define morphisms and discuss hyperbolicity. For this purpose we establish a Brody theorem for orbifolds. Using this Brody theorem for orbifolds we then determine which one-dimensional orbifolds are hyperbolic. We also show in the last section that some of the weakly special but not special projective threefolds constructed by Bogomolov-Tschinkel have a non-vanishing Kobayashi pseudometric. There are two different classes of orbifold morphisms, baptised "classical'', and "non-classcal''. In the "classical sense'' many problems are easier to handle because "classical'' orbifold morphisms behave very well with respect to etale orbifold morphisms. In particular, the classification of one-dimensional hyperbolic orbifolds can be obtained via "unfoldings''. In contrast, for determining which one-dimensional orbifolds are hyperbolic in the "non-classical'' sense we really need our ``Brody theorem for orbifolds''.

Domaines: Géométrie algébrique [math.AG]

Frédéric Campana, Jörg Winkelmann. A brody theorem for orbifolds. 2006. ⟨hal-00091386⟩