Nonarchimedean coamoeba of a line in space

    Here is the non-Archimedean coamoeba of the line
x+&zetay2t  =  ix+z-(1+i)  =  0 .
ζ is a primitive cube root of 1 and i2=-1.
    The tropical variety of the line has four rays in the coordinate directions—their initial varieties give the four boundary edges of this coamoeba.
    There are two trivalent (hence planar) vertices—their initial varieties give two pairs of triangles, which are coamoeba of planar lines.
    Lastly, there is one internal edge whose initial variety gives the line common to the two sets of triangles.

Eight fundamental domains.

Last modified: Wed Mar 16 11:30:32 CET 2011