Generalized logarithmic Gauss map and its relation to (co)amoebas

We define the generalized logarithmic Gauss map for algebraic varieties of the complex algebraic torus of any codimension. Moreover, we describe the set of critical points of the logarithmic mapping restricted to our variety, and we show an analogous of Mikhalkin's result on the critical points of the logarithmic map restricted to a hypersurfaces.