Analytic Varieties with Finite Volume Amoebas are Algebraic

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Date
2011MFO Scientific Program
OWLF 2011Series
Oberwolfach Preprints;2011,33Author
Madani, Farid
Nisse, Mounir
Metadata
Show full item recordOWP-2011-33
Abstract
In this paper, we study the amoeba volume of a given $k$-dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba is finite. Moreover, in this case, we establish a comparison theorem for the volume of the amoeba and the coamoeba. Examples and applications to the $k$-linear spaces will be given.