Vol. 7, No. 2, 2013

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The phase limit set of a variety

Mounir Nisse and Frank Sottile

Vol. 7 (2013), No. 2, 339–352
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/