Polynomial bounds for rings of invariants

Derksen, Harm

doi:10.1090/S0002-9939-00-05698-7

Polynomial bounds for rings of invariants
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Proc. Amer. Math. Soc. 129 (2001), 955-963 Request permission

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 $d$ such that the invariants of degree $\leq d$ 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.

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