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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the characterization of algebraically integrable plane foliations
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by C. Galindo and F. Monserrat PDF
Trans. Amer. Math. Soc. 362 (2010), 4557-4568 Request permission


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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Additional Information
  • 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:
  • F. Monserrat
  • Affiliation: Instituto Universitario de Matemática Pura y Aplicada, Universidad Politécnica de Valencia, Camino de Vera s/n, 46022 Valencia, Spain
  • MR Author ID: 738424
  • Email:
  • 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
  • © Copyright 2010 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 362 (2010), 4557-4568
  • MSC (2010): Primary 32S65
  • DOI:
  • MathSciNet review: 2645041