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- W4300693635 abstract "Let $R$ be a local commutative noetherian ring and $HKR$ the homology ring of the corresponding Koszul 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 it does 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 {tt BERGMAN} by Jorgen Backelin et al, the {tt Macaulay2}-package {tt DGAlgebras} by Frank Moore, combined with results by Govorov, Clas Lofwall, Victor Ufnarovski and others." @default.
- W4300693635 created "2022-10-04" @default.
- W4300693635 creator A5034665878 @default.
- W4300693635 date "2015-12-30" @default.
- W4300693635 modified "2023-10-03" @default.
- W4300693635 title "Homological Properties of the Homology Algebra of the Koszul Complex of a Local Ring. Examples and Questions" @default.
- W4300693635 doi "https://doi.org/10.48550/arxiv.1512.09188" @default.
- W4300693635 hasPublicationYear "2015" @default.
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