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An approach to plane algebroid branches

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Abstract

We consider a new approach to the local geometry of plane algebraic curves that allows us to obtain the basic results of the theory of plane algebroid branches over algebraically closed fields of arbitrary characteristic. We do not use the Hamburger-Noether expansions. Our basic tool is the logarithmic distance on the set of branches satisfying the strong triangle inequality which permits to make calculations directly on the equations of branches.

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Notes

  1. Quoted after Samuel E. Stumpf. Socrates to Sartre. A History of Philosophy. Mc Graw-Hill, Inc. 1993.

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Acknowledgments

The authors are very grateful to the anonymous referees for the improvement of this paper.

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Authors and Affiliations

  1. Departamento de Matemáticas, Estadística e Investigación Operativa, Sección de Matemáticas, Universidad de La Laguna, 38271 , La Laguna, Tenerife, Spain

    Evelia Rosa García Barroso

  2. Department of Mathematics, Kielce University of Technology, Al. 1000 L PP7, 25-314 , Kielce, Poland

    Arkadiusz Płoski

Authors
  1. Evelia Rosa García Barroso
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  2. Arkadiusz Płoski
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Correspondence to Evelia Rosa García Barroso.

Additional information

The E. R. García Barroso was partially supported by the Spanish Project PNMTM 2007-64007.

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García Barroso, E.R., Płoski, A. An approach to plane algebroid branches. Rev Mat Complut 28, 227–252 (2015). https://doi.org/10.1007/s13163-014-0155-5

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