Degree bounds on homology and a conjecture of Derksen. (21st September 2016)

• Record Type: Journal Article
• Authors: Chardin, Marc; Symonds, Peter
• Is Part Of: Compositio mathematica. Volume 152:Number 10(2016)
• Page Start: 2041
• Page End: 2049
• Publication Date: 2016-09-21
• Subjects: 13D02, -- 13A50 (primary); invariant theory, -- degree bounds, -- local cohomology; Mathematics -- Periodicals; 510
• DOI: 10.1112/S0010437X16007430
• Languages: English
• ISSNs: 0010-437X

Abstract

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.