1. Contact exponent and the Milnor number of plane curve singularities
- Author
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Evelia Rosa Garcia Barroso, Arkadiusz Płoski, Krasiński, Tadeusz, Spodzieja, Stanisław, Departamento de Matematicas, Estadistica e I.O. Seccion de Matematicas, Universidad de La Laguna Apartado de Correos 456, and Department of Mathematics and Physics, Kielce University of Technology
- Subjects
Mathematics::Algebraic Geometry - Abstract
We investigate properties of the contact exponent (in the sense of Hironaka [Hi]) of plane algebroid curve singularities over algebraically closed fields of arbitrary characteristic. We prove that the contact exponent is an equisingularity invariant and give a new proof of the stability of the maximal contact. Then we prove a bound for the Milnor number and determine the equisingularity class of algebroid curves for which this bound is attained. We do not use the method of Newton's diagrams. Our tool is the logarithmic distance developed in [GB-P1].
- Published
- 2019