Polynomial bounds for rings of invariants

Abstract

Hilbert proved that invariant rings are finitely generated for linearly reductive groups acting rationally on a finite dimensional vector space. Popov gave an explicit upper bound for the smallest integer d d such that the invariants of degree ≤ d \leq d generate the invariant ring. This bound has factorial growth. In this paper we will give a bound which depends only polynomially on the input data.