Contact exponent and Milnor number of plane curve singularities.

  1. Evelia R. García Barroso 1
  2. Arkadiusz P. Loski
  1. 1 Universidad de La Laguna
    info

    Universidad de La Laguna

    San Cristobal de La Laguna, España

    ROR https://ror.org/01r9z8p25

Book:
Analytic and Algebraic Geometry, 3.

Publisher: Łódź University Press

ISBN: 978-83-8142-814-9

Year of publication: 2019

Pages: 93-109

Type: Book chapter

DOI: 10.18778/8142-814-9.08 GOOGLE SCHOLAR lock_openOpen access editor

Abstract

We investigate properties of the contact exponent (in the sense ofHironaka [Hi]) of plane algebroid curve singularities over algebraically closedfields of arbitrary characteristic. We prove that the contact exponent is anequisingularity invariant and give a new proof of the stability of the maximalcontact. Then we prove a bound for the Milnor number and determine theequisingularity class of algebroid curves for which this bound is attained. Wedo not use the method of Newton’s diagrams. Our tool is the logarithmicdistance developed in [GB-P1].