On the Factorization of the Polar of a Plane Branch

  • A. HefezEmail author
  • M. E. Hernandes
  • M. F. H. Iglesias
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 222)


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.


Polar curves Polar decomposition Equisingularity 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • A. Hefez
    • 1
    Email author
  • M. E. Hernandes
    • 2
  • M. F. H. Iglesias
    • 3
  1. 1.Universidade Federal FluminenseSão Francisco, NiteróiBrazil
  2. 2.Universidade Estadual de MaringáMaringáBrazil
  3. 3.Universidade Federal FluminenseNiteroiBrazil

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