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arXiv · 2508.17572

Bernstein polynomial and value set of differentials for plane branches

Andrea Gomes Guimarães·Marcelo Escudeiro Hernandes
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Abstract

In this work, we study the relation between the roots of the Bernstein polynomial $\widetilde{b}$ and the value set of differentials $\Lambda$ for plane branches. For plane branches defined by semiquasihomogeneous polynomial we describe the set of common roots of $\widetilde{b}$ sharing by every branch with a fixed $\Lambda$ set.

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Andrea Gomes Guimarães, Marcelo Escudeiro Hernandes. 2025-08-25. Bernstein polynomial and value set of differentials for plane branches. https://arxiv.org/abs/2508.17572

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