Algebra structures on minimal resolutions of Gorenstein rings of embedding codimension four

DOI10.1007/BF01159957zbMath0419.13013OpenAlexW2002239268MaRDI QIDQ1132136

Andrew R. Kustin, Matthew P. Miller

Publication date: 1980

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/172977

zbMATH Keywords

Gorenstein local ringminimal finite free resolutiondifferential graded commutative algebras

Mathematics Subject Classification ID

Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Resolutions; derived functors (category-theoretic aspects) (18G10) Ideals and multiplicative ideal theory in commutative rings (13A15) Modules of differentials (13N05)

Related Items (25)

Gorenstein ideals of deviation two ⋮ Linkage theory for algebras with pure resolutions ⋮ Deformation and Linkage of Gorenstein Algebras ⋮ Lower Bounds on Betti Numbers ⋮ Applications of Differential Graded Algebra Techniques in Commutative Algebra ⋮ Free resolutions and change of rings ⋮ Poincaré series of modules over local rings of small embedding codepth or small linking number ⋮ Use DG-methods to build a matrix factorization ⋮ Tom and Jerry triples with an application to Fano 3-folds ⋮ Algebra structures on some canonical resolutions ⋮ Persistence of homology over commutative Noetherian rings ⋮ Deformations of half-canonical Gorenstein curves in codimension four ⋮ Spinor structures on free resolutions of codimension four Gorenstein ideals ⋮ Gorenstein algebras of codimension four and characteristic two ⋮ The Cramer varieties \(\mathrm{Cr}(r,r+s,s)\) ⋮ Structure Theory for a Class of Grade Four Gorenstein Ideals ⋮ Resolutions of length four which are differential graded algebras ⋮ The non-existence of a minimal algebra resolution despite the vanishing of Avramov obstructions ⋮ Classification of the Tor-Algebras of Codimension Four Almost Complete Intersections ⋮ The Structure Theorem for Complete Intersections of Grade 4 ⋮ The DG products of Peeva and Srinivasan coincide ⋮ Constructing big Gorenstein ideals from small ones ⋮ A Somewhat Gentle Introduction to Differential Graded Commutative Algebra ⋮ The Poincaré series of a codimension four Gorenstein ring is rational ⋮ Minimal algebra resolutions for cyclic modules defined by Huneke-Ulrich ideals

Cites Work

• Liaison des variétés algébriques. I
• Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay
• On the ubiquity of Gorenstein rings
• The Map of the Witt Ring of a Domain into the Witt Ring of its Field of Fractions
• Algebra Structures for Finite Free Resolutions, and Some Structure Theorems for Ideals of Codimension 3
• Specialization of quadratic and symmetric, bilinear forms, and a norm theorem
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