Newton polytopes of invariants of additive group actions

Abstract

It is shown that the vertices of Newton polytopes of invariants of an algebraic group action of the additive group of a field k of arbitrary characteristic on affine n-space over k lie on the coordinate hyperplanes. Furthermore, let E be the set of all edges of these Newton polytopes whose vertices lie in different coordinate hyperplanes. It is shown that one of these polytopes has edges with all directions represented in E.