NDLI: On Discrete groups of automorphisms of $$\mathbb P ^2

Content Provider	Springer Nature Link
Author	Ca, Angel Seade, José
Copyright Year	2013
Abstract	We study the geometry and dynamics of discrete subgroups $$\Gamma $$ of $$\mathrm{PSL}(3,\mathbb C )$$ with an open invariant set $$\Omega \subset \mathbb P _\mathbb{C }^2$$ where the action is properly discontinuous and the quotient $$\Omega /\Gamma $$ contains a connected component whicis compact. We call such groups quasi-cocompact. In this case $$\Omega /\Gamma $$ is a compact complex projective orbifold and $$\Omega $$ is a divisible set. Our first theorem refines classical work by Kobayashi–Ochiai and others about complex surfaces with a projective structure: We prove that every such group is either virtually affine or complex hyperbolic. We then classify the divisible sets that appear in this way, the corresponding quasi-cocompact groups and the orbifolds $$\Omega /\Gamma $$ . We also prove that excluding a few exceptional cases, the Kulkarni region of discontinuity coincides with the equicontinuity region and is the largest open invariant set where the action is properly discontinuous.
Ending Page	60
Page Count	52
Starting Page	9
File Format	PDF
ISSN	00465755
e-ISSN	15729168
Journal	Geometriae Dedicata
Issue Number	1
Volume Number	168
Language	English
Publisher	Springer Netherlands
Publisher Date	2013-01-08
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Geometry Fuchsian groups and their generalizations Equicontinuity Group actions in low dimensions Complex Kleinian groups Kleinian groups Properly discontinuous actions Limit set Complex hyperbolic groups Complex affine groups
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology

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