On unique and almost unique factorization of complete ideals. II

DOI10.1007/BF01388844zbMath0715.13012MaRDI QIDQ752088

Steven Dale Cutkosky

Publication date: 1989

Published in: Inventiones Mathematicae (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/143720

zbMATH Keywords

UFDbirational morphismblow-upscomplete normal local domaincomplete primary ideals

Mathematics Subject Classification ID

Singularities in algebraic geometry (14B05) Rational and birational maps (14E05) Ideals and multiplicative ideal theory in commutative rings (13A15) Commutative rings defined by factorization properties (e.g., atomic, factorial, half-factorial) (13F15)

Related Items (30)

When are the blow ups of two ideals the same scheme? ⋮ Indecomposable integrally closed modules of arbitrary rank over a two-dimensional regular local ring ⋮ Multiplicities and Mixed Multiplicities of Filtrations ⋮ Zeros of Differentials Along One-Fibered Ideals ⋮ Factorization of complete ideals in normal birational extensions in dimension two ⋮ A new characterization of rational surface singularities ⋮ Examples of multiplicities and mixed multiplicities of filtrations ⋮ Ideal theory in two-dimensional regular local domains and birational extensions ⋮ Open Problems in Commutative Ring Theory ⋮ Integral closure and other operations on monomial ideals ⋮ Positivity of mixed multiplicities of filtrations ⋮ On Finite and Nonfinite Generation of Associated Graded Rings of Abhyankar Valuations ⋮ A local version of some results of zariski ⋮ Searching for Cutkosky's example ⋮ Symmetric powers of complete modules over a two-dimensional regular local ring ⋮ Asymptotic behavior of Ext functors for modules of finite complete intersection dimension ⋮ Arcs and wedges on rational surface singularities ⋮ Blowups in tame monomial ideals ⋮ Discrete valuations centered on local domains ⋮ Integrally closed and componentwise linear ideals ⋮ Graded rings associated with contracted ideals ⋮ Some results relating to adjacent ideals in dimension two ⋮ A mixed multiplicity formula for complete ideals in 2-dimensional rational singularities ⋮ The Minkowski equality of filtrations ⋮ First neighborhood complete ideals in two-dimensional Muhly local domains are projectively full ⋮ Poincaré series of resolutions of surface singularities ⋮ Mixed multiplicities of filtrations ⋮ Unique factorization of *-products of one-fibered monomial ideals ⋮ Mixed multiplicities of divisorial filtrations ⋮ ANALYTIC SPREAD OF FILTRATIONS ON TWO-DIMENSIONAL NORMAL LOCAL RINGS

Cites Work

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• Weil divisors on normal surfaces
• Factorization of complete ideals
• The topology of normal singularities of an algebraic surface and a criterion for simplicity
• Semifactoriality and Muhly's condition (N) in two dimensional local rings
• Rational singularities, with applications to algebraic surfaces and unique factorization
• Some Numerical Criteria for Contractability of Curves on Algebraic Surfaces
• Asymptotic Factorization of Ideals
• ON A CONJECTURE OF SAMUEL
• On the Existence of Asymptotically Irreducible Ideals
• Polynomial Ideals Defined by Infinitely Near Base Points
• Reduction of the singularities of algebraic three dimensional varieties

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