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Polynomial bounds for rings of invariants


Author: Harm Derksen
Journal: Proc. Amer. Math. Soc. 129 (2001), 955-963
MSC (2000): Primary 13A50
DOI: https://doi.org/10.1090/S0002-9939-00-05698-7
Published electronically: October 20, 2000
MathSciNet review: 1814136
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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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Additional Information

Harm Derksen
Affiliation: Department of Mathematics, Massachusetts Institute of Technology 77, Massachusetts Avenue, Cambridge, Massachusetts 02139
Email: hderksen@math.mit.edu

DOI: https://doi.org/10.1090/S0002-9939-00-05698-7
Received by editor(s): July 8, 1999
Published electronically: October 20, 2000
Additional Notes: The author was partially supported by the Swiss National Science Foundation (SNF) and the Freiwillige Akademische Gesellschaft.
Communicated by: Michael Stillman
Article copyright: © Copyright 2000 American Mathematical Society

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