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arXiv · 1205.2808

Amoebas and coamoebas of linear spaces

Mounir Nisse·Mikael Passare
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Abstract

We give a complete description of amoebas and coamoebas of $k$-dimensional very affine linear spaces in $(\mathbb{C}^*)^{n}$. This include an upper bound of their dimension, and we show that if a $k$-dimensional very affine linear space in $(\mathbb{C}^*)^{n}$ is generic, then the dimension of its (co)amoeba is equal to $\min \{ 2k, n\}$. Moreover, we prove that the volume of its coamoeba is equal to $\pi^{2k}$. In addition, if the space is generic and real, then the volume of its amoeba is equal to $\frac{\pi^{2k}}{2^k}$.

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Mounir Nisse, Mikael Passare. 2012-05-12. Amoebas and coamoebas of linear spaces. https://arxiv.org/abs/1205.2808

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