The Minimal Free Resolution of the Migliore–Peterson Rings in the Case That the Reflexive Sheaf Has Even Rank

Kustin, Andrew R.

doi:10.1006/jabr.1998.7484

Cited by 2 publications

(3 citation statements)

References 12 publications

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“…(ii) Let r be even and let t = 1. This case was also studied by Kustin [9]; his main result gives (up to the degree shifts) the same resolution as our Theorem 5.8 (cf. also Corollary 5.13).…”

Section: Some Vector Bundles Of Low Rank and Their Sectionssupporting

confidence: 69%

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Buchsbaum–Rim Sheaves and Their Multiple Sections

Migliore¹,

Nagel²,

Peterson³

1999

Journal of Algebra

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This paper begins by introducing and characterizing Buchsbaum-Rim sheaves on Z = Proj R, where R is a graded Gorenstein K-algebra. They are reflexive sheaves arising as the sheafification of kernels of sufficiently general maps between free Rmodules. Then we study multiple sections of a Buchsbaum-Rim sheaf ϕ , i.e, we consider morphisms ψ → ϕ of sheaves on Z dropping rank in the expected codimension, where H 0 * Z is a free R-module. The main purpose of this paper is to study properties of schemes associated to the degeneracy locus S of ψ. It turns out that S is often not equidimensional. Let X denote the top-dimensional part of S. In this paper we measure the "difference" between X and S, compute their cohomology modules and describe ring-theoretic properties of their coordinate rings. Moreover, we produce graded free resolutions of X (and S) which are in general minimal. Among the applications we show how one can embed a subscheme into an arithmetically Gorenstein subscheme of the same dimension and prove that zero-loci of sections of the dual of a null correlation bundle are arithmetically Buchsbaum.

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Section: Some Vector Bundles Of Low Rank and Their Sectionssupporting

confidence: 69%

“…(ii) In case t = 1 and r is even the result has been first proved by the first and third author who communicated it to Kustin. Subsequently, Kustin [9] strengthened it by removing almost all the assumptions on the ring R and computing a free resolution (cf. also Remark 5.10 and Corollary 5.13).…”

Section: It Has Already Been Observed Inmentioning

confidence: 99%

Buchsbaum–Rim Sheaves and Their Multiple Sections

Migliore¹,

Nagel²,

Peterson³

1999

Journal of Algebra

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“…Write IW im W Ì S and JW IW unm , which is the intersection of the primary components of IW having maximal dimension. As B Ã im J 1 , one has S=I W > SE, and since E satis®es G 1 one concludes that height I W r and S=JW > RE The ideals I W and JW however were studied in [40] and [38] (notice that r > 2 since proj dim E > 1; in [40] the modules are assumed to be graded over a homogeneous ring, but this assumption can be deleted). Now I W JW (that is, E is of linear type) if and only if r is even [40, 4.5.a].…”

Section: Small Dimensionsmentioning

confidence: 99%

Rees Algebras of Modules

Simis

Ulrich

Vasconcelos

2003

Proc. London Math. Soc.

122

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We study Rees algebras of modules within a fairly general framework. We introduce an approach through the notion of Bourbaki ideals that allows the use of deformation theory. One can talk about the (essentially unique) generic Bourbaki ideal I(E) of a module E which, in many situations, allows one to reduce the nature of the Rees algebra of E to that of its Bourbaki ideal I(E). Properties such as Cohen–Macaulayness, normality and being of linear type are viewed from this perspective. The known numerical invariants, such as the analytic spread, the reduction number and the analytic deviation, of an ideal and its associated algebras are considered in the case of modules. Corresponding notions of complete intersection, almost complete intersection and equimultiple modules are examined in some detail. Special consideration is given to certain modules which are fairly ubiquitous because interesting vector bundles appear in this way. For these modules one is able to estimate the reduction number and other invariants in terms of the Buchsbaum–Rim multiplicity. 2000 Mathematics Subject Classification 13A30 (primary), 13H10, 13B21 (secondary)

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The Minimal Free Resolution of the Migliore–Peterson Rings in the Case That the Reflexive Sheaf Has Even Rank

Cited by 2 publications

References 12 publications

Buchsbaum–Rim Sheaves and Their Multiple Sections

Buchsbaum–Rim Sheaves and Their Multiple Sections

Rees Algebras of Modules

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