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Homological Properties of the Homology Algebra of the Koszul Complex of a Local Ring. Examples and Questions.
Stockholm University, Faculty of Science, Department of Mathematics. (algebra)
(English)Manuscript (preprint) (Other academic)
Abstract [en]

Let R be a local commutative noetherian ring and HKR the homology ring of the correspondingKoszul complex. We study the homological properties of HKR in particular the so-called Avramov spectral sequence. When the embedding dimension of R is four and when R can be presented with quadratic relations we have found 102 cases where this spectral sequence degenerates and only three cases where itdoes not degenerate. We also determine completely the Hilbert series of the bigraded Tor of these HKR in tables A-D of section 5. We also study some higher embedding dimensions. Among the methods used are the programme BERGMAN by Jörgen Backelin et al, the Macaulay2-package DGAlgebras by Frank Moore,combined with results by Govorov, Clas Löfwall, Victor Ufnarovski and others.

National Category
Algebra and Logic
Research subject
URN: urn:nbn:se:su:diva-124643OAI: diva2:890425
local ring, Koszul complex, Gorenstein rings, Yoneda Ext-algebra, Hilbert series, Macaulay2, programme BERGMAN
Available from: 2016-01-03 Created: 2016-01-03 Last updated: 2016-01-03

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Roos, Jan-Erik
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Department of Mathematics
Algebra and Logic

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