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Degree bounds on homology and a conjecture of Derksen

Part of: General commutative ring theory Commutative algebra: Homological methods

Published online by Cambridge University Press:  21 September 2016

Marc Chardin  and
Peter Symonds
Marc Chardin
Affiliation:
Institut de Mathématiques de Jussieu, 4, place Jussieu, F-75005 Paris, France email marc.chardin@imj-prg.fr
Peter Symonds
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK email Peter.Symonds@manchester.ac.uk
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Abstract

Harm Derksen made a conjecture concerning degree bounds for the syzygies of rings of polynomial invariants in the non-modular case [Degree bounds for syzygies of invariants, Adv. Math. 185 (2004), 207–214]. We provide counterexamples to this conjecture, but also prove a slightly weakened version. We also prove some general results that give degree bounds on the homology of complexes and of $\text{Tor}\,$ groups.

Keywords

invariant theorydegree boundslocal cohomology

MSC classification

Primary: 13D02: Syzygies, resolutions, complexes 13A50: Actions of groups on commutative rings; invariant theory

Information

Type
Research Article
Information
Compositio Mathematica , Volume 152 , Issue 10 , October 2016 , pp. 2041 - 2049
Copyright
© The Authors 2016 

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