On amoebas of algebraic sets of higher codimension

The amoeba of a complex algebraic set is its image under the projection onto the real subspace in the logarithmic scale. We study the homological properties of the complements of amoebas for sets of codimension higher than 1. In particular, we refine A. Henriques' result saying that the complement of the amoeba of a codimension $k$ set is $(k-1)$-convex. We also describe the relationship between the critical points of the logarithmic projection and the logarithmic Gauss map of algebraic sets.