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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.Date of publication of this fulltext: 07 Feb 2012 09:49
Monograph
DOI to cite this document: 10.5283/epub.23411
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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Details
| Item type | Monograph (Working Paper) | ||||||
| Series of the University of Regensburg: | Preprintreihe der Fakultät Mathematik | ||||||
|---|---|---|---|---|---|---|---|
| Volume: | 4/2012 | ||||||
| Date | 2012 | ||||||
| Institutions | Mathematics > Prof. Dr. Bernd Ammann | ||||||
| Classification |
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| Keywords | Analytic varieties, algebraic varieties, amoebas, coamoebas, logarithmic limit sets, phase limit sets, spherical polyhedrons | ||||||
| Dewey Decimal Classification | 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 | ||||||
| URN of the UB Regensburg | urn:nbn:de:bvb:355-epub-234114 | ||||||
| Item ID | 23411 |
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