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The analytic classification of plane curves

Part of: Curves Singularities

Published online by Cambridge University Press:  19 March 2024

Marcelo Escudeiro Hernandes Open the ORCID record for Marcelo Escudeiro Hernandes [Opens in a new window]  and
Maria Elenice Rodrigues Hernandes Open the ORCID record for Maria Elenice Rodrigues Hernandes [Opens in a new window]
Marcelo Escudeiro Hernandes
Affiliation:
Universidade Estadual de Maringá, Av. Colombro 5790, Maringá-Pr 87020-900, Brazil [email protected]
Maria Elenice Rodrigues Hernandes
Affiliation:
Universidade Estadual de Maringá, Av. Colombro 5790, Maringá-Pr 87020-900, Brazil [email protected]
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Abstract

In this paper, we present a solution to the problem of the analytic classification of germs of plane curves with several irreducible components. Our algebraic approach follows precursive ideas of Oscar Zariski and as a subproduct allows us to recover some particular cases found in the literature.

Keywords

plane curvesanalytic classificationanalytic invariants

MSC classification

Primary: 14H20: Singularities, local rings
Secondary: 14H10: Families, moduli (algebraic) 32S05: Local singularities 32S10: Invariants of analytic local rings
Type
Research Article
Information
Compositio Mathematica , Volume 160 , Issue 4 , April 2024 , pp. 915 - 944
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Copyright
© 2024 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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Footnotes

The authors were partially supported by grant 2019/07316-0, São Paulo Research Foundation (FAPESP) and the first author was partially supported by CNPq-Brazil Proc. 303638/2020-6.

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