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Conformal Geometry and Dynamics

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Construction of vector fields and Riccati foliations associated to groups of projective automorphisms


Authors: Fabio Santos and Bruno Scárdua
Journal: Conform. Geom. Dyn. 14 (2010), 154-166
MSC (2010): Primary 37F75, 32S65; Secondary 32M25, 32M05
DOI: https://doi.org/10.1090/S1088-4173-2010-00208-0
Published electronically: June 2, 2010
MathSciNet review: 2652067
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Abstract | References | Similar Articles | Additional Information

Abstract: Our main result states that given a finitely generated subgroup $ G$ of $ \operatorname{Aut}(\mathbb{C} P (2))$, there is an algebraic foliation $ \mathcal{F}$ on a complex projective $ 3$-manifold $ M^3$ with a bundle structure over $ \mathbb{C} P(1)$ and fiber $ \mathbb{C} P(2)$, such that $ \mathcal{F}$ is transverse to almost every fiber of the bundle and with global holonomy conjugate to $ G$.


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Additional Information

Fabio Santos
Affiliation: Departamento de Geometria, Instituto de Matemática, Universidade Federal Fluminense, Niteroi, Rio de Janeiro 24.020-140, Brazil
Email: fabio@mat.uff.br

Bruno Scárdua
Affiliation: Instituto de Matematica, Universidade Federal do Rio de Janeiro, CP. 68530-Rio de Janeiro-RJ, 21945-970, Brazil
Email: scardua@im.ufrj.br

DOI: https://doi.org/10.1090/S1088-4173-2010-00208-0
Keywords: Holomorphic foliation, holonomy, projective automorphism
Received by editor(s): August 27, 2009
Published electronically: June 2, 2010
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.