Tropical geometry of phase limit set of the plane

    These four components of the phase limit set correspond to the four rays of the tropical variety (here a fan) of the plane. It is interesting to note that the union of (the closures of) these four components of the phase limit set is the (closure of) the coamoeba, and a general point of the coamoeba lies in exactly two of these phase limit sets.
    There are higher-codimensional pieces of the phase limit set which correspond to the six two-dimensional cones in the tropical fan. Each of these is a 2-dimensional subtorus, which is one of the six facets of the coamoeba. Observe that parts of these components are on the boundary of the coamoeba, and parts lie within the interior of the coamoeba.
Return to Chalk Talk



Last modified: Wed Mar 30 18:20:30 CEST 2011