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Transactions of the American Mathematical Society

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On the characterization of algebraically integrable plane foliations


Authors: C. Galindo and F. Monserrat
Journal: Trans. Amer. Math. Soc. 362 (2010), 4557-4568
MSC (2010): Primary 32S65
DOI: https://doi.org/10.1090/S0002-9947-10-04808-7
Published electronically: April 27, 2010
MathSciNet review: 2645041
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Abstract: We give a characterization theorem for non-degenerate plane foliations of degree different from 1 having a rational first integral. Moreover, we prove that the degree $ r$ of a non-degenerate foliation as above provides the minimum number, $ r+1$, of points in the projective plane through which pass infinitely many algebraic leaves of the foliation.


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C. Galindo
Affiliation: Departamento de Matemáticas and Instituto Universitario de Matemáticas y Aplicaciones de Castellón (IMAC), Universidad Jaume I, Campus Riu Sec, 12071 Castellón, Spain
Email: galindo@mat.uji.es

F. Monserrat
Affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
Email: framonde@mat.upv.es

DOI: https://doi.org/10.1090/S0002-9947-10-04808-7
Received by editor(s): November 10, 2006
Received by editor(s) in revised form: April 18, 2008
Published electronically: April 27, 2010
Additional Notes: The first author was supported by the Spain Ministry of Education MTM2007-64704 and Bancaixa P1-1B2009-03
The second author was supported by the Spain Ministry of Education MTM2007-64704 and Bancaixa P1-1A2005-08
Article copyright: © Copyright 2010 American Mathematical Society

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