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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A formula relating inflections, bitangencies and the Milnor number of a plane curve


Authors: Fabio Scalco Dias, Raúl Oset Sinha and Maria Aparecida Soares Ruas
Journal: Proc. Amer. Math. Soc. 142 (2014), 2353-2368
MSC (2010): Primary 14H20; Secondary 53A55, 58K60
Published electronically: March 31, 2014
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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.


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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
Email: maasruas@icmc.usp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2014-11980-0
PII: S 0002-9939(2014)11980-0
Keywords: Milnor number, plane curves, double point, inflection, bitangency.
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
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.