Madani, Farid and Nisse, Mounir (2012) Analytic varieties with finite volume amoebas are algebraic. Preprintreihe der Fakultät Mathematik 4/2012, Working Paper.
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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|Item Type:||Monograph (Working Paper)|
|Institutions:||Mathematics > Prof. Dr. Bernd Ammann|
|Keywords:||Analytic varieties, algebraic varieties, amoebas, coamoebas, logarithmic limit sets, phase limit sets, spherical polyhedrons|
|Dewey Decimal Classification:||500 Science > 510 Mathematics|
|Refereed:||No, this version has not been refereed yet (as with preprints)|
|Created at the University of Regensburg:||Yes|
|Deposited On:||07 Feb 2012 09:49|
|Last Modified:||13 Mar 2014 18:34|