On the volume of complex amoebas

Authors:
Farid Madani and Mounir Nisse

Journal:
Proc. Amer. Math. Soc. **141** (2013), 1113-1123

MSC (2010):
Primary 14T05, 32A60

DOI:
https://doi.org/10.1090/S0002-9939-2012-11394-2

Published electronically:
August 17, 2012

MathSciNet review:
3008859

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Abstract | References | Similar Articles | Additional Information

Abstract: The paper deals with amoebas of -dimensional algebraic varieties in the complex algebraic torus of dimension . First, we show that the area of complex algebraic curve amoebas is finite. Moreover, we give an estimate of this area in the rational curve case in terms of the degree of the rational parametrization coordinates. We also show that the volume of the amoeba of a -dimensional algebraic variety in , with , is finite.

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Additional Information

**Farid Madani**

Affiliation:
NWF I-Mathematik, Universität Regensburg, 93040 Regensburg, Germany

Email:
Farid.Madani@mathematik.uni

**Mounir Nisse**

Affiliation:
Department of Mathematics, Texas A&M University, College Station, Texas 77843-3368

Email:
nisse@math.tamu.edu

DOI:
https://doi.org/10.1090/S0002-9939-2012-11394-2

Keywords:
Algebraic varieties,
amoebas,
logarithmic limit sets

Received by editor(s):
February 11, 2011

Received by editor(s) in revised form:
August 6, 2011

Published electronically:
August 17, 2012

Additional Notes:
The first author is supported by the Alexander von Humboldt Foundation.

The research of the second author is partially supported by NSF MCS grant DMS-0915245.

Dedicated:
Dedicated to the memory of Mikael Passare (1959–2011)

Communicated by:
Lev Borisov

Article copyright:
© Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.