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arXiv · 2402.08301

H\"older invariance of the Henry-Parusinski invariant

Alexandre Fernandes·José Edson Sampaio·Joserlan Perote da Silva
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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.

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Alexandre Fernandes, José Edson Sampaio, Joserlan Perote da Silva. 2024-02-13. H\"older invariance of the Henry-Parusinski invariant. https://arxiv.org/abs/2402.08301

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