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Degree bounds on homology and a conjecture of Derksen

Published online by Cambridge University Press:  21 September 2016

Marc Chardin
Affiliation:
Institut de Mathématiques de Jussieu, 4, place Jussieu, F-75005 Paris, France email [email protected]
Peter Symonds
Affiliation:
School of Mathematics, University of Manchester, Manchester M13 9PL, UK email [email protected]
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Abstract

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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.

Type
Research Article
Copyright
© The Authors 2016 

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