Buchsbaum Rings and Applications

Stückrad, Jürgen; Vogel, Wolfgang

doi:10.1007/978-3-662-02500-0

Cited by 268 publications

(159 citation statements)

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“…A comprehensive reference to Buchsbaum rings and modules is [31]. Here we will need only a few standard properties that we record in the following lemma.…”

Section: Homologically Isolated Singularitiesmentioning

confidence: 99%

Face numbers of pseudomanifolds with isolated singularities

Novik¹,

Swartz²

2012

MATH. SCAND.

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We investigate the face numbers of simplicial complexes with Buchsbaum vertex links, especially pseudomanifolds with isolated singularities. This includes deriving Dehn-Sommerville relations for pseudomanifolds with isolated singularities and establishing lower and upper bound theorems when the singularities are also homologically isolated. We give formulas for the Hilbert function of a generic Artinian reduction of the face ring when the singularities are homologically isolated and for any pure two-dimensional complex. Some examples of spaces where the f -vector can be completely characterized are described. We also show that the Hilbert function of a generic Artinian reduction of the face ring of a simplicial complex with isolated singularities minus the h-vector of is a PL-topological invariant.

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“…A comprehensive reference to Buchsbaum rings and modules is [31]. Here we will need only a few standard properties that we record in the following lemma.…”

Section: Homologically Isolated Singularitiesmentioning

confidence: 99%

Face numbers of pseudomanifolds with isolated singularities

Novik¹,

Swartz²

2012

MATH. SCAND.

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“…The importance of the existence of a standard ideal is made clear by the following proposition, for which we refer the reader to [SV,Corollary 18,p. 264].…”

Section: Proof Of the Main Theorem And A Corollarymentioning

confidence: 99%

“…, y n )A. The ring A does not have finite local cohomologies since its minimal primes xA and p have different dimensions: dim A/(x) = n and dim A/p = 1 [SV,Proposition 16,p. 260].…”

Section: Proposition 41 [Eg Theorem A]mentioning

confidence: 99%

The Index of Reducibility of Parameter Ideals and Mostly Zero Finite Local Cohomologies

Liu

Rogers

2006

Communications in Algebra

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Abstract. In this paper we prove that if M is a finitely-generated module of dimension d with finite local cohomologies over a Noetherian local ring (A, m), and if H i m (M ) = 0 except possibly for i ∈ {0, r, d} with some 0 ≤ r ≤ d, then there exists an integer ℓ such that every parameter ideal for M contained in m ℓ has the same index of reducibility. This theorem generalizes earlier work of the second author and is closely related to recent work of GotoSuzuki and Goto-Sakurai; Goto-Sakurai have supplied an answer of yes in case M is Buchsbaum.

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“…We will often use the following duality result (cf. [31], [33]) without further mentioning. Proposition 2.2.…”

Section: Preliminariesmentioning

confidence: 99%

“…This is an important concept which has its origin in a negative answer of Vogel [34] to a problem of Buchsbaum. It has been stimulating intensive research (cf., for example, [32] and in particular [33]). A new characterization of arithmetically Buchsbaum subschemes is given by the following result (cf.…”

Section: Introductionmentioning

confidence: 99%

Characterization of some projective subschemes by locally free resolutions

Nagel¹

2003

Commutative Algebra

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Abstract. A locally free resolution of a subscheme is by definition an exact sequence consisting of locally free sheaves (except the ideal sheaf) which has uniqueness properties like a free resolution. The purpose of this paper is to characterize certain locally Cohen-Macaulay subschemes by means of locally free resolutions. First we achieve this for arithmetically Buchsbaum subschemes. This leads to the notion of an Ω-resolution and extends the main result of Chang in [6]. Second we characterize quasi-Buchsbaum subschemes by means of weak Ω-resolutions. Finally, we describe the weak Ω-resolutions which belong to arithmetically Buchsbaum surfaces of codimension two. Various applications of our results are given.

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Buchsbaum Rings and Applications

Cited by 268 publications

References 0 publications

Face numbers of pseudomanifolds with isolated singularities

Face numbers of pseudomanifolds with isolated singularities

The Index of Reducibility of Parameter Ideals and Mostly Zero Finite Local Cohomologies

Characterization of some projective subschemes by locally free resolutions

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