On Macaulayfication of Noetherian schemes

DOI10.1090/S0002-9947-00-02603-9zbMath0954.14032OpenAlexW1718701227MaRDI QIDQ4955696

Takesi Kawasaki

Publication date: 22 May 2000

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-00-02603-9

zbMATH Keywords

desingularization\(d\)-sequenceblowing-updualizing complexMacaulayficationNoetherian schemeCohen-Macaulay scheme\(p\)-standard system of parametersSharp's conjecture

Mathematics Subject Classification ID

Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) (14M05) Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) (13H10) Singularities in algebraic geometry (14B05) Global theory and resolution of singularities (algebro-geometric aspects) (14E15)

Related Items (34)

dd-SEQUENCES AND PARTIAL EULER–POINCARÉ CHARACTERISTICS OF KOSZUL COMPLEX ⋮ Testing for the Gorenstein property ⋮ On Injective and Gorenstein Injective Dimensions of Local Cohomology Modules ⋮ Frobenius test exponents for parameter ideals in generalized Cohen-Macaulay local rings ⋮ On theS₂-Fication of Some Toric Varieties ⋮ Linearity defects of modules over commutative rings ⋮ Existence of Gorenstein projective resolutions and Tate cohomology ⋮ Ascent properties for test modules ⋮ Partially ample subvarieties of projective varieties ⋮ On almost p-standard system of parameters of idealization and applications ⋮ When does a perturbation of the equations preserve the normal cone? ⋮ On the uniform bound of reducibility index of parameter ideals of idealizations ⋮ On the partial Euler-Poincaré characteristics of Koszul complexes of idealization ⋮ Generalized Serre conditions and perverse coherent sheaves ⋮ Characterizing Gorenstein rings using contracting endomorphisms ⋮ Cohen factorizations: weak functoriality and applications ⋮ Hilbert coefficients and partial Euler-Poincaré characteristics of Koszul complexes of d-sequences ⋮ Homological dimensions and semidualizing complexes ⋮ On the structure of sequentially generalized Cohen-Macaulay modules ⋮ Local cohomology annihilators and Macaulayfication ⋮ On arithmetic Macaulayfication of Noetherian rings ⋮ Noether resolutions in dimension 2 ⋮ Singularities and perfectoid geometry ⋮ Finiteness of cousin cohomologies ⋮ Macaulayfication of Noetherian schemes ⋮ Perverse coherent sheaves and the geometry of special pieces in the unipotent variety. ⋮ Local cohomology based on a nonclosed support defined by a pair of ideals ⋮ On the localization theorem for \(F\)-pure rings ⋮ Sequentially Cohen-Macaulay Modules Under Base Change ⋮ Classification of dominant resolving subcategories by moderate functions ⋮ The Index of Reducibility of Parameter Ideals and Mostly Zero Finite Local Cohomologies ⋮ Arithmetic Macaulayfication of projective schemes ⋮ Extensions of a dualizing complex by its ring: Commutative versions of a conjecture of Tachikawa ⋮ On maps of Grothendieck groups induced by completion.

Uses Software

• Macaulay2

Cites Work

• Unnamed Item
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• Two types of birational models
• Dualizing complexes and systems of parameters
• Existence of dualizing complexes
• Some special cases of a conjecture of Sharp
• On Buchsbaum rings
• Dualisierende Komplexe in der lokalen Algebra und Buchsbaum-Ringe
• Computation of Hilbert functions
• Certain graded algebras are always Cohen-Macaulay
• Über die Annulatoren lokaler Kohomologiegruppen
• On graded rings. I
• Über Macaulayfizierung. (On macaulayfication)
• On Macaulayfication of certain quasi-projective schemes
• \(p\)-standard systems of parameters and \(p\)-standard ideals in local rings
• The theory of d-sequences and powers of ideals
• Residues and duality. Lecture notes of a seminar on the work of A. Grothendieck, given at Havard 1963/64. Appendix: Cohomology with supports and the construction of the \(f^!\) functor by P. Deligne
• Resolution of singularities of an algebraic variety over a field of characteristic zero. I
• A few remarks on blowing-up and connectedness.
• Standard systems of parameters and their blowing-up rings.
• Cohomological annihilators
• On the Cohen-Macaulayfication of certain Buchsbaum rings
• The Converse to a Theorem of Sharp on Gorenstein Modules

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