On the Volume of Complex Amoebas

Details On the Volume of Complex Amoebas On the Volume of Complex Amoebas

2011-01-25

arxiv.org/abs/1101.4693v1

Mathematics

Algebraic Geometry

10 pages, 2 figures

Scientific paper

The paper deals with amoebas of $k$-dimensional algebraic varieties in the algebraic complex 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 $k$-dimensional algebraic variety in $(\mathbb{C}^*)^{n}$, with $n\geq 2k$, is finite.

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