Separating monomials for diagonalizable actions

TL;DR

This paper characterizes sets of monomials that distinguish Zariski closed orbits under diagonalizable group actions using zero-sum sequences, and compares degree bounds for separating and generating invariants.

Contribution

It introduces a characterization of separating monomials via zero-sum sequences and applies this to compare degree bounds for invariants.

Findings

Characterization of separating monomials using zero-sum sequences.

Comparison of degree bounds for separating and generating invariants.

Application to diagonalizable group 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.