Separating monomials for diagonalizable actions

Abstract

Sets of monomials separating Zariski closed orbits under diagonalizable group actions are characterized in terms of the monoid of zero-sum sequences over the character group. This is applied to compare the degree bounds for separating invariants and generating invariants of diagonalizable group actions.

Version 3: references added to Section 4 and minor editing. Version 2: Related prior results of Dufresne and Jeffries are taken into account. Some of the statements are sharpened or generalized. Monoid theoretic content is clarified