Even Liaison Classes Generated by Gorenstein Linkage

Nagel, Uwe

doi:10.1006/jabr.1998.7524

Cited by 29 publications

(60 citation statements)

References 21 publications

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“…In the presence of G 1 , this makes E reflexive [3, 1.9]. Thus, the extraverti sheaves of (1.12)c are reflexive, and we recover the construction of Nollet [13] and Nagel [12] by another route.…”

Section: ) There Is a Closed Subsetsupporting

confidence: 56%

On Rao's theorems and the Lazarsfeld-Rao property

Hartshorne¹

2003

Annales De La Faculté Des Sciences De Toulouse Mathématiques

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Let X be an integral projective scheme satisfying the condition S 3 of Serre and H 1 (O X (n)) = 0 for all n ∈ Z. We generalize Rao's theorem by showing that biliaison equivalence classes of codimension two subschemes without embedded components are in one-to-one correspondence with pseudo-isomorphism classes of coherent sheaves on X satisfying certain depth conditions.We give a new proof and generalization of Strano's strengthening of the Lazarsfeld-Rao property, showing that if a codimension two subscheme is not minimal in its biliaison class, then it admits a strictly descending elementary biliaison.For a three-dimensional arithmetically Gorenstein scheme X, we show that biliaison equivalence classes of curves are in one-to-one correspondence with triples (M, P, α), up to shift, where M is the Rao module, P is a maximal Cohen-Macaulay module on the homogeneous coordinate ring of X, and α : P ∨ → M * → 0 is a surjective map of the duals.Proposition 1.11. Every psi equivalence class of sheaves satisfying T contains an extraverti sheaf satisfying T .Proof. Let E be a coherent sheaf satisfying T . Let), and hence is a finitely generated graded S = H 0 * (O X )-module. Take a set of generators ξ i ∈ Ext 1 (E, O X (−a i )) of this module and let

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Section: ) There Is a Closed Subsetsupporting

confidence: 56%

On Rao's theorems and the Lazarsfeld-Rao property

Hartshorne¹

2003

Annales De La Faculté Des Sciences De Toulouse Mathématiques

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“…In [14] the unmixedness of an ideal of R has been characterized by means of its local cohomology modules. First we note that this result can be extended to finitely generated R-modules.…”

Section: Unmixedness Resultsmentioning

confidence: 99%

Bezout's theorem and Cohen-Macaulay modules

Migliore¹,

Nagel²,

Peterson³

2001

Math Z

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Abstract. We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect properly. We prove a Bezout theorem for modules which meet very properly. Furthermore, we show for equidimensional subschemes X and Y : If they intersect properly in an arithmetically Cohen-Macaulay subscheme of positive dimension then X and Y are arithmetically Cohen-Macaulay. The module version of this result implies splitting criteria for reflexive sheaves.

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“…On the other hand the property is preserved in the whole even liaison of I according to [26], Theorem 3.10. Now we want to formulate the consequences of Theorem 4.6 for an arithmetically Buchsbaum subscheme X ⊂ P n = P n K .…”

Section: Theorem 52 With the Notation Above The Following Conditionmentioning

confidence: 93%

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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Even Liaison Classes Generated by Gorenstein Linkage

Cited by 29 publications

References 21 publications

On Rao's theorems and the Lazarsfeld-Rao property

On Rao's theorems and the Lazarsfeld-Rao property

Bezout's theorem and Cohen-Macaulay modules

Characterization of some projective subschemes by locally free resolutions

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