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Relative Canonical Sheaves of a Family of Curves

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Jongmin Lee

Algebraic Geometry · Submitted 18 Nov 2002

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

The authors' main claim In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m > 1.

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arXiv IDmath/0211274 (version 1)
Pith ID5LGCCBGF, Pith's permanent record of this paper and its review
CitationJongmin Lee. "Relative Canonical Sheaves of a Family of Curves." arXiv:math/0211274 (2002). https://pith.science/paper/5LGCCBGF
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,307 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.14 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.95 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m > 1. We use Koszul cohomology with it to prove that the relative canonical ring of the fibration is generated in degree up to five.

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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 In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m > 1. result 0.98 0.95 0.90 asserted 1.00
s1 We use Koszul cohomology with it to prove that the relative canonical ring of the fibration is generated in degree up to five. method 0.48 0.92 0.08 asserted 1.00

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

In this paper we show that the relative canonical sheaf of a relatively minimal fibration of curves over a curve is semi-ample ; in fact, its m-tensored product is base point free for any m > 1. We use Koszul cohomology with it to prove that the relative canonical ring of the fibration is generated in degree up to five.

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