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The Lattice of Amoebas

descriptionPublicationkeyboard_double_arrow_right Article , Preprint 01 Jan 2017Embargo end date: 01 Jan 2017Publisher:arXiv

Authors: Forsgård, Jens; de Wolff, Timo;

doi: 10.48550/arxiv.1711.02705

arXiv: http://arxiv.org/abs/1711.02705

The Lattice of Amoebas

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Abstract

We study amoebas of exponential sums as functions of the support set $A$. 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.

15 pages, 2 figures

Keywords

Mathematics - Algebraic Geometry, Mathematics - Complex Variables, FOS: Mathematics, Mathematics - Combinatorics, Combinatorics (math.CO), Complex Variables (math.CV), Algebraic Geometry (math.AG)

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