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April 2015 On the order map for hypersurface coamoebas
Jens Forsgård, Petter Johansson
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Ark. Mat. 53(1): 79-104 (April 2015). DOI: 10.1007/s11512-013-0195-y

Abstract

Given a hypersurface coamoeba of a Laurent polynomial f, it is an open problem to describe the structure of the set of connected components of its complement. In this paper we approach this problem by introducing the lopsided coamoeba. We show that the closed lopsided coamoeba comes naturally equipped with an order map, i.e. a map from the set of connected components of its complement to a translated lattice inside the zonotope of a Gale dual of the point configuration $\operatorname{supp}(f)$. Under a natural assumption, this map is a bijection. Finally we use this map to obtain new results concerning coamoebas of polynomials of small codimension.

Dedication

In memory of Mikael Passare, who continues to inspire.

Citation

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Jens Forsgård. Petter Johansson. "On the order map for hypersurface coamoebas." Ark. Mat. 53 (1) 79 - 104, April 2015. https://doi.org/10.1007/s11512-013-0195-y

Information

Received: 8 February 2013; Revised: 15 August 2013; Published: April 2015
First available in Project Euclid: 30 January 2017

zbMATH: 1354.32003
MathSciNet: MR3319615
Digital Object Identifier: 10.1007/s11512-013-0195-y

Rights: 2014 © Institut Mittag-Leffler

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Vol.53 • No. 1 • April 2015
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