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VOL. 42 | 2004 Amoebas, convexity and the volume of integer polytopes
Mikael Passare

Editor(s) Kimio Miyajima, Mikio Furushima, Hideaki Kazama, Akio Kodama, Junjiro Noguchi, Takeo Ohsawa, Hajime Tsuji, Tetsuo Ueda

Abstract

To any given Laurent polynomial $f$ on $\mathbf{C}_{*}^{n}$ we associate two natural convex functions $M_f$ and $N_f$ on $\mathbf{R}^n$. We compute the Hessian of $M_f$ and obtain an explicit formula for the volume of the Newton polytope $\Delta_f$. We also establish asymptotic formulas relating our convex functions to coherent triangulations of $\Delta_f$ and to the secondary polytope.

Information

Published: 1 January 2004
First available in Project Euclid: 3 January 2019

zbMATH: 1068.14061
MathSciNet: MR2087057

Digital Object Identifier: 10.2969/aspm/04210263

Rights: Copyright © 2004 Mathematical Society of Japan

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