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Vector flows and the analytic moduli of singular plane branches

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

We provide a geometric elementary proof of the fact that an analytic plane branch is analytically equivalent to one whose terms corresponding to contacts with holomorphic one-forms—except for Zariski’s \(\lambda \)-invariant— are zero (so called “short parametrizations”). This is the main step missed by Zariski in his attempt to solve the moduli problem.

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Acknowledgements

The redaction of this paper has improved greatly thanks to an anonymous reviewer.

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Authors and Affiliations

  1. Department of Mathematics, University of Oviedo, Oviedo, Spain

    P. Fortuny Ayuso

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  1. P. Fortuny Ayuso
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Correspondence to P. Fortuny Ayuso.

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To Prof. Felipe Cano on his sixtieth birthday.

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Fortuny Ayuso, P. Vector flows and the analytic moduli of singular plane branches. RACSAM 113, 4107–4118 (2019). https://doi.org/10.1007/s13398-019-00665-w

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  • DOI: https://doi.org/10.1007/s13398-019-00665-w

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