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arXiv · 2010.09492

Examples on the sharpness of an inequality about multiplicities over hyperfields

Ziqi Liu
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Abstract

In this paper, the author introduces hyperfields and give some facts about the roots and multiplicities of polynomials over hyperfield based on \cite{2} and \cite{3}. Then he tests the sharpness of an inequality in Baker's former work \cite{2} about the behavior of multiplicities under homomorphisms between hyperfields and show that the inequality is not sharp under the natural homomorphisms $\mathbb{C}\rightarrow\mathbb{P}$ and $\mathbb{C}\rightarrow\mathbb{V}$ while it is sharp under the natural homomorphisms $\mathbb{C}\rightarrow\mathbb{K}$, $\mathbb{R}\rightarrow\mathbb{S}$ and $\mathbb{R}\rightarrow\mathbb{T}$ according to the previous work \cite{2} of Baker and Lorscheid.

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Ziqi Liu. 2020-10-16. Examples on the sharpness of an inequality about multiplicities over hyperfields. https://doi.org/10.13140/rg.2.2.22666.70089

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