Year: 2026
Type: article
Abstract: We prove that, except for two explicit families, every discrete subgroup $$G \subset \textrm{PSL}(3,\mathbb {C})$$ G ⊂ PSL ( 3 , C ) that acts properly discontinuously on a non-empty open subset of $$\mathbb{C}\mathbb{P}^2$$ C P 2 admits a unique largest $$G$$ G -invariant open set $$\Omega _G \subset \mathbb{C}\mathbb{P}^2$$ Ω G ⊂ C P 2 on which the action is properly discontinuous. We refer to $$\Omega _G$$ Ω G as the regular set of $$G$$ G . We also establish several geometric and analytic properties of $$\Omega _G$$ Ω G and compare its complement with other natural limit sets associated to the action.
Authors: Angel Cano, Laura A. Cano Cordero, Luis Loeza
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,190
OpenAlex ID: W7161979096