Newton polyhedra and toroidal varieties

The toroidal compactification (C~0)~f ~ plays the same role as the projective compactification ~ P ~ in the classical case. Toroidal varieties are well known [2, 3]. It is almost as easy to handle them as projective spaces. In a subsequent paper the geometry of toroidal varieties will be used for the calculation of the arithmetic genus and Euler characteristic of variety X. Here we discuss the connection of this geometry with the elementary geometry of integral polyhedra.