On Discrete Subgroups of automorphism of $P^2_C$

Mathematics – Dynamical Systems

Scientific paper

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38 pages

Scientific paper

In this work we study discrete subgroups $\Gamma$ of $PSL_3(\Bbb{C})$ and some of their basic properties. We show that if there is a region of "discontinuity" of the action of $\Gamma$ on $\Bbb{P}^2_{\Bbb{C}}$ which contains $\Gamma$-cocompact components, then the group is either elementary, affine or fuchsian. Moreover, there is a largest open set on which $\Gamma$ acts properly discontinuously.

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