Coamoeba of a symmetric line in 3-space

Coamoeba of a symmetric line in 3-space

The coamoeba of the highly symmetric line in (C*)³,
t --> (t-1, t-ζ, t-ζ²), (ζ is a primitive third root of 1) is a 2-dimensional membrane whose boundary consists of four lines, one parallel to each of the coordinate directions. (It contains no points of these lines.)

It does contain a number of other lines, and its projection in any coordinate direction is the two triangles that we saw of a line in the plane.

Eight fundamental domains.

Last modified: Mon Sep 12 13:38:22 CDT 2011