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arXiv · 1905.08056

On the number of intersection points of the contour of an amoeba with a line

Lionel Lang·Boris Shapiro·Eugenii Shustin
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Abstract

In this note, we investigate the maximal number of intersection points of a line with the contour of hypersurface amoebas in $\mathbb{R}^n$. We define the latter number to be the $\mathbb{R}$-degree of the contour. We also investigate the $\mathbb{R}$-degree of related sets such as the boundary of amoebas and the amoeba of the real part of hypersurfaces defined over $\mathbb{R}$. For all these objects, we provide bounds for the respective $\mathbb{R}$-degrees.

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Lionel Lang, Boris Shapiro, Eugenii Shustin. 2019-05-20. On the number of intersection points of the contour of an amoeba with a line. https://arxiv.org/abs/1905.08056

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