Higher convexity of amoebas and coamoebas
Mounir Nisse and
Frank Sottile
The amoebae A below
(la tour Eiffel à trois pieds) is the amoeba of a line in
(C*)3.
Notice how its complement is not convex, in fact neither of the two components is convex.
However, the pictures show that if you intersect the complement with an affine plane
L,
then we have an injection of first homology groups,
H1(L∩ R3-A)
→
H1(R3-A) .
We may also look at coamoebae of lines in (C*)3, on the
next page.
Last modified: Wed Jun 11 20:43:33 CDT 2014
