H\"older invariance of the Henry-Parusinski invariant

Alexandre Fernandes; José Edson Sampaio; Joserlan Perote da Silva

H\"older invariance of the Henry-Parusinski invariant

Algebraic Geometry 2024-02-14 v1 Complex Variables

Authors: Alexandre Fernandes , José Edson Sampaio , Joserlan Perote da Silva

Abstract

In this article, we show the H\"older invariance of the Henry-Parusinski invariant. For a single germ $f$ , the Henry-Parusinski invariant of $f$ is given in terms of the leading coefficients of the asymptotic expansion of $f$ along the branches of the generic polar curve of $f$ . As a consequence, we obtain that the classification problem of polynomial function-germs, with uniformly bounded degree, under H\"older equivalence, admits continuous moduli.

Keywords

henry-parusinski invariant h"older invariance polynomial function-germs asymptotic expansion polar curve classification problem continuous moduli

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@article{arxiv.2402.08301,
  title  = {H\"older invariance of the Henry-Parusinski invariant},
  author = {Alexandre Fernandes and José Edson Sampaio and Joserlan Perote da Silva},
  journal= {arXiv preprint arXiv:2402.08301},
  year   = {2024}
}

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19 pages

H\"older invariance of the Henry-Parusinski invariant

Abstract

Keywords

Cite

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