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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A formula relating inflections, bitangencies and the Milnor number of a plane curve
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by Fabio Scalco Dias, Raúl Oset Sinha and Maria Aparecida Soares Ruas PDF
Proc. Amer. Math. Soc. 142 (2014), 2353-2368 Request permission

Abstract:

In this article we obtain a formula relating inflections, bitangencies and the Milnor number of a plane curve germ. Moreover, we present an extension of the formula obtained by the first author and Luis Fernando Mello for a class of plane curves with singularities.
References
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Additional Information
  • Fabio Scalco Dias
  • Affiliation: Instituto de Ciências Exatas, Universidade Federal de Itajubá, Avenida BPS 1303, Pinheirinho, CEP 37.500–903, Itajubá, MG, Brazil
  • Email: scalco@unifei.edu.br
  • Raúl Oset Sinha
  • Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, CEP 13.560–970, São Carlos-SP, Brazil
  • Email: raul.oset@uv.es
  • Maria Aparecida Soares Ruas
  • Affiliation: Departamento de Matemática, Instituto de Ciências Matemáticas e de Computação, Universidade de São Paulo, CEP 13.560–970, São Carlos-SP, Brazil
  • MR Author ID: 239264
  • ORCID: 0000-0001-8890-524X
  • Email: maasruas@icmc.usp.br
  • Received by editor(s): November 11, 2011
  • Received by editor(s) in revised form: August 5, 2012
  • Published electronically: March 31, 2014
  • Additional Notes: The first author was supported by FAPESP grant No. 2011/01946-0.
    The second author was partially supported by FAPESP grant No. 2010/01501-5 and DGCYT and FEDER grant No. MTM2009-08933
    The third author was supported by FAPESP, grant No. 08/54222-6 and CNPq, grant No. 303774/2008-8.
  • Communicated by: Lev Borisov
  • © Copyright 2014 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 142 (2014), 2353-2368
  • MSC (2010): Primary 14H20; Secondary 53A55, 58K60
  • DOI: https://doi.org/10.1090/S0002-9939-2014-11980-0
  • MathSciNet review: 3195759