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