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Analytic varieties with finite volume amoebas are algebraic

Madani, Farid and Nisse, Mounir (2012) Analytic varieties with finite volume amoebas are algebraic. Preprintreihe der Fakultät Mathematik 4/2012, Working Paper.

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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.


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Item Type:Monograph (Working Paper)
Date:2012
Institutions:Mathematics > Prof. Dr. Bernd Ammann
Classification:
NotationType
14T05MSC
32A60MSC
Keywords:Analytic varieties, algebraic varieties, amoebas, coamoebas, logarithmic limit sets, phase limit sets, spherical polyhedrons
Subjects:500 Science > 510 Mathematics
Status:Unknown
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
Item ID:23411
Owner Only: item control page

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