a1 Universidad Autónoma de Yucatán, Facultad de Matematicas, Periférico Norte Tablaje Cat 13615 Chuburná Hildalgo, Mérida, Yucatán, México. e-mail: email@example.com
a2 Instituto de Matemática Pura e Aplicada, Estrada Dona Castorina 110, Rio de Janeiro, Brazil. e-mail: firstname.lastname@example.org
a3 Universidad Autónoma de Yucatán, Facultad de Matematicas, Periférico Norte Tablaje Cat 13615 Chuburná Hildalgo, Mérida, Yucatán, México. e-mail: email@example.com
If Γ is a discrete subgroup of PSL(3, ℂ), it is determined the equicontinuity region Eq(Γ) of the natural action of Γ on ℙ2ℂ. It is also proved that the action restricted to Eq(Γ) is discontinuous, and Eq(Γ) agrees with the discontinuity set in the sense of Kulkarni whenever the limit set of Γ in the sense of Kulkarni, Λ(Γ), contains at least three complex lines in general position. Under some additional hypothesis, it turns out to be the largest open set on which Γ acts discontinuously. Moreover, if Λ(Γ) contains at least four complex lines and Γ acts on ℙ2ℂ without fixed points nor invariant complex lines, then each connected component of Eq(Γ) is a holomorphy domain and a complete Kobayashi hyperbolic space.
(Received January 11 2010)
(Online publication September 02 2010)