Non-archimedean amoebas and tropical varieties
Algebraic Geometry
2015-12-23 v2 Commutative Algebra
Dynamical Systems
Abstract
We study the non-archimedean counterpart to the complex amoeba of an algebraic variety, and show that it coincides with a polyhedral set defined by Bieri and Groves using valuations. For hypersurfaces this set is also the tropical variety of the defining polynomial. Using non-archimedean analysis and a recent result of Conrad we prove that the amoeba of an irreducible variety is connected. We introduce the notion of an adelic amoeba for varieties over global fields, and establish a form of the local-global principle for them. This principle is used to explain the calculation of the nonexpansive set for a related dynamical system.
Cite
@article{arxiv.math/0408311,
title = {Non-archimedean amoebas and tropical varieties},
author = {Manfred Einsiedler and Mikhail Kapranov and Douglas Lind},
journal= {arXiv preprint arXiv:math/0408311},
year = {2015}
}
Comments
19 pages, 2 figures. Added AIM preprint number