On the volume of complex amoebas

Madani, Farid; Nisse, Mounir

doi:10.1090/S0002-9939-2012-11394-2

On the volume of complex amoebas
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by Farid Madani and Mounir Nisse PDF

Proc. Amer. Math. Soc. 141 (2013), 1113-1123 Request permission

Abstract:

The paper deals with amoebas of $k$-dimensional algebraic varieties in the complex algebraic torus of dimension $n\geq 2k$. First, we show that the area of complex algebraic curve amoebas is finite. Moreover, we give an estimate of this area in the rational curve case in terms of the degree of the rational parametrization coordinates. We also show that the volume of the amoeba of a $k$-dimensional algebraic variety in $(\mathbb {C}^*)^{n}$, with $n\geq 2k$, is finite.

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