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
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.