Higher convexity of coamoeba complements

Abstract

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.

14 pages, 5 color figures, minor revisions