Newton polytopes of constants of locally nilpotent derivations

The Newton polytopes of constants of locally nilpotent derivations of the a lgebra of polynomials in several commuting variables over a field of charac teristic zero are considered. It is shown that the vertices of these polyto pes lie on the coordinate hyperplanes. A complete description of all possib le edges of these polytopes is obtained. In the two variable case Rentschle r's classification of locally nilpotent derivations is obtained as a coroll ary.