Corpus ID: 159041378

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

@article{Lang2019OnTN,
  title={On the number of intersection points of the contour of an amoeba with a line},
  author={Lionel Lang and B. Shapiro and E. Shustin},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
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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