On the factorization of the polar of a plane branch

A. Hefez, M. E. Hernandes, M. F.H. Iglesias

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

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.

Original languageEnglish
Title of host publicationSingularities and Foliations. Geometry, Topology and Applications - BMMS 2/NBMS 3
EditorsJawad Snoussi, Raimundo Nonato Araujo dos Santos, Marcelo J. Saia, David Mond, Aurelio Menegon Neto
PublisherSpringer New York LLC
Pages347-362
Number of pages16
ISBN (Print)9783319736389
DOIs
StatePublished - 2018
Event2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015 - Salvador, Brazil
Duration: 13 Jul 201517 Jul 2015

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume222
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Conference

Conference2nd Brazil-Mexico Meeting on Singularity and 3rd Northeastern Brazilian Meeting on Singularities, BMMS 2/NBMS 3 2015
CountryBrazil
CitySalvador
Period13/07/1517/07/15

Bibliographical note

Funding Information:
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.

Publisher Copyright:
© Springer International Publishing AG, part of Springer Nature 2018.

Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.

Keywords

  • Equisingularity
  • Polar curves
  • Polar decomposition

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