Higher convexity of coamoeba complements

Understand

We show that the complement of the coamoeba of a variety of codimension k+1 is k-convex, in the sense of Gromov and Henriques.

• This generalizes a result of Nisse for hypersurface coamoebas.
• We use this to show that the complement of the nonarchimedean coamoeba of a variety of codimension k+1 is k-convex.