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Characterization of some projective subschemes by locally free resolutions

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Uwe Nagel

Commutative Algebra · Submitted 16 Dec 2002

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim The purpose of this paper is to characterize certain locally Cohen-Macaulay subschemes by means of locally free resolutions.

how it is stated · asserted 0.91 read the record →

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arXiv IDmath/0212217 (version 1)
Pith IDKJ6AMXMB, Pith's permanent record of this paper and its review
CitationUwe Nagel. "Characterization of some projective subschemes by locally free resolutions." arXiv:math/0212217 (2002). https://pith.science/paper/KJ6AMXMB
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 5,422 input tokens.

What the abstract itself states, as probabilities: claims first 0.09 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.75 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

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 $\Omega$-resolution and extends a result of Chang. Second we characterize quasi-Buchsbaum subschemes by means of weak $\Omega$-resolutions. Finally, we describe the weak $\Omega$-resolutions which belong to arithmetically Buchsbaum surfaces of codimension two. Various applications of our results are given.

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What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 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. background 1.00 0.05 0.03 asserted 1.00
s1 The purpose of this paper is to characterize certain locally Cohen-Macaulay subschemes by means of locally free resolutions. contribution 0.97 0.52 0.15 asserted 0.91
s2 First we achieve this for arithmetically Buchsbaum subschemes. contribution 0.81 0.91 0.07 asserted 1.00
s3 This leads to the notion of an $\Omega$-resolution and extends a result of Chang. contribution 0.73 0.88 0.12 asserted 1.00
s4 Second we characterize quasi-Buchsbaum subschemes by means of weak $\Omega$-resolutions. contribution 0.80 0.94 0.18 asserted 1.00
s5 Finally, we describe the weak $\Omega$-resolutions which belong to arithmetically Buchsbaum surfaces of codimension two. contribution 0.80 0.93 0.14 asserted 1.00
s6 Various applications of our results are given. contribution 0.87 0.85 0.05 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original 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 $\Omega$-resolution and extends a result of Chang. Second we characterize quasi-Buchsbaum subschemes by means of weak $\Omega$-resolutions. Finally, we describe the weak $\Omega$-resolutions which belong to arithmetically Buchsbaum surfaces of codimension two. Various applications of our results are given.

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