Homological Properties of the Homology Algebra of the Koszul Complex of a Local Ring. Examples and Questions.
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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.
Algebra and Logic
Research subject Mathematics
IdentifiersURN: urn:nbn:se:su:diva-124643OAI: oai:DiVA.org:su-124643DiVA: diva2:890425
Projectslocal ring, Koszul complex, Gorenstein rings, Yoneda Ext-algebra, Hilbert series, Macaulay2, programme BERGMAN