CoAmoebae in 3-space

Mounir Nisse and Frank Sottile
A coamoeba is the image of a subvariety of the torus (C*)n under the argument map to (S1)n. CoAmoebae exhibit structure that is both polyhdral and curvilinear. Below, we show the coamoebae of a line and a plane in (C*)3. The links are to further pictures and discussion.

CoAmoeba of the line t --> (t-1, t-ζ, t2),
where ζ is a primitive third root of 1.

More coAmoebae of lines in (C*)3.

CoAmoeba of the plane x+y+z+1 =0 in (C*)3.
The coAmoeba of the plane and its phase-limit set.
Last modified: Sat Dec 4 09:44:04 CST 2010