Higher convexity of coamoeba complements

nisse, mounir; sottile, frank;

We show that the complement of the closure 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.