2015/12/30 by Jan-Erik Roos, Roos, Jan-Erik
Mathematics · #16S37 (Secondary) #68W30 (Primary) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1512.09188
openalex publication_date 2015/12/30 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
Let R be a local commutative noetherian ring and HKR the homology ring of\nthe corresponding Koszul complex. We study the homological properties of HKR\nin particular the so-called Avramov spectral sequence. When the embedding\ndimension of R is four and when R can be presented with quadratic relations\nwe have found 102 cases where this spectral sequence degenerates and only three\ncases where it does not degenerate. We also determine completely the Hilbert\nseries of the bigraded Tor of these HKR in tables A-D of section 5. We also\nstudy some higher embedding dimensions. Among the methods used are the\nprogramme tt BERGMAN by J "orgen Backelin et al, the tt Macaulay2-package\n tt DGAlgebras by Frank Moore, combined with results by Govorov, Clas\nL "ofwall, Victor Ufnarovski and others.\n