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Analytic varieties with finite volume amoebas are algebraic

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Madani, Farid ; Nisse, Mounir
Date of publication of this fulltext: 07 Feb 2012 09:49


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.

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