The Optimal Lower Bound for Generators of Invariant Rings without Finite SAGBIBases with Respect to Any Admissible Order

Abstract

We prove the existence of an invariant ring C[X 1,...,X n ] T generated by elements with a total degree of at most 2, which has no finite SAGBI basis with respect to any admissible order. Therefore, 2 is the optimal lower bound for the total degree of generators of invariant rings with such a property.