Abstract
Irreducible complex plane curve germs with the same characteristic exponents form an equisingularity class. In this paper we determine the Zariski invariants that characterize the general polar of a general member of such an equisingularity class. More precisely, we will describe explicitly the characteristic exponents of the irreducible components of the polar and their mutual intersection multiplicities, allowing us in particular to describe completely the content of each of Merle’s packages of the polar.
A. Hefez and M. E. Hernandes were partially supported by the CNPq grants 307873/2016-1 and 303594/2014-4, respectively, while the third author was supported by a fellowship from CAPES/Fundação Araucária.
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References
Casas-Alvero, E.: Singularities of Plane Curves. Cambridge University Press (2000)
Casas-Alvero, E.: On the singularities of polar curves. Manuscripta Math. 43, 167–190 (1983)
Casas-Alvero, E.: Infinitely near imposed singularities and singularities of polar curves. Math. Ann. 287, 429–454 (1990)
Enriques, F., Chisini, O.: Lezioni sulla teoria geometrica delle equazioni e delle funzioni algebriche. N. Zanichelli, Bologna (1915)
Hefez, A., Hernandes, M.E., Iglesias, M.F.H.: On polars of plane branches. In: Singularities in Geometry, Topology, Foliations and Dynamics. Trends in Mathematics, pp. 135–153. Birkhäuser (2017)
Hefez, A., Hernandes, M.E., Iglesias, M.F.H.: Plane branches with Newton nondegenerate polars. arxiv: 160.07522 [math.AG]
Merle, M.: Invariants polaires des courbes planes. Inventiones Mathematicae 41, 103–111 (1977)
Pham, F.: Deformations equisingulières des idéaux jacobiens des courbes planes. In: Proceedings of Liverpool Symposium on Singularities II of Lecturer Notes in Mathematics, vol. 209, pp. Springer, New York (1971)
Teissier, B.: Variétés polaires I: Invariants polaires des singularités d’hypersurfaces. Inventiones Mathematicae 41(3), 267–292 (1977)
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Hefez, A., Hernandes, M.E., Iglesias, M.F.H. (2018). On the Factorization of the Polar of a Plane Branch. In: Araújo dos Santos, R., Menegon Neto, A., Mond, D., Saia, M., Snoussi, J. (eds) Singularities and Foliations. Geometry, Topology and Applications. NBMS BMMS 2015 2015. Springer Proceedings in Mathematics & Statistics, vol 222. Springer, Cham. https://doi.org/10.1007/978-3-319-73639-6_11
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DOI: https://doi.org/10.1007/978-3-319-73639-6_11
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