The phase limit set of a variety

Nisse, Mounir; Sottile, Frank

doi:10.2140/ant.2013.7.339

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The phase limit set of a variety

Mounir Nisse and Frank Sottile

Vol. 7 (2013), No. 2, 339–352

DOI: 10.2140/ant.2013.7.339

Abstract

A coamoeba is the image of a subvariety of a complex torus under the argument map to the real torus. We describe the structure of the boundary of the coamoeba of a variety, which we relate to its logarithmic limit set. Detailed examples of lines in three-dimensional space illustrate and motivate these results.

Keywords

coamoeba, amoeba, initial ideal, toric variety tropical geometry

Mathematical Subject Classification 2010

Primary: 14T05

Secondary: 32A60

Milestones

Received: 7 June 2011

Revised: 14 February 2012

Accepted: 16 March 2012

Published: 25 April 2013

Authors

Mounir Nisse
Department of Mathematics Texas A&M University College Station, TX 77843 United States
http://www.math.tamu.edu/~nisse/
Frank Sottile
Department of Mathematics Texas A&M University College Station, TX 77843 United States
http://www.math.tamu.edu/~sottile/

Vol. 7, No. 2, 2013