The Lattice of Amoebas
Algebraic Geometry
2018-11-13 v2 Combinatorics
Complex Variables
Abstract
We study amoebas of exponential sums as functions of the support set . To any amoeba, we associate a set of approximating sections of amoebas, which we call caissons. We show that a bounded modular lattice of subspaces of a certain vector space induces a lattice structure on the set of caissons. Our results unifies the theories of lopsided amoebas and amoebas of exponential sums. As an application, we show that our theory of caissons yields improved certificates for existence of certain components of the complement of an amoeba.
Keywords
Cite
@article{arxiv.1711.02705,
title = {The Lattice of Amoebas},
author = {Jens Forsgård and Timo de Wolff},
journal= {arXiv preprint arXiv:1711.02705},
year = {2018}
}
Comments
15 pages, 2 figures