Newton polytopes and irreducible components of complete intersections

We calculate the number of irreducible components of varieties in $(\mathbb C^*)^n$ determined by generic systems of equations with given Newton polytopes. Every such component can in its turn be given by a generic system of equations whose Newton polytopes are found explicitly. It is known that many discrete invariants of a variety can be found in terms of the Newton polytopes. Our results enable one to calculate such invariants for each irreducible component of the variety.