On the volume of complex amoebas
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- by Farid Madani and Mounir Nisse PDF
- Proc. Amer. Math. Soc. 141 (2013), 1113-1123 Request permission
Abstract:
The paper deals with amoebas of $k$-dimensional algebraic varieties in the complex algebraic torus of dimension $n\geq 2k$. 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 $k$-dimensional algebraic variety in $(\mathbb {C}^*)^{n}$, with $n\geq 2k$, is finite.References
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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
- 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. - Communicated by: Lev Borisov
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3008859
Dedicated: Dedicated to the memory of Mikael Passare (1959–2011)