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A contraction theorem for divisors fibering over a curve

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Andreas Höring, Thomas Peternell

Algebraic Geometry · Submitted 24 Sep 2024

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

The authors' main claim Given a Q-Cartier divisor $S \subset X$ admitting a fibration $S \rightarrow B$ onto a curve we give sufficient conditions for the existence of a bimeromorphic contraction contracting S onto B.

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arXiv ID2409.15993 (version 1)
Pith IDXIV6DOSQ, Pith's permanent record of this paper and its review
CitationAndreas H\"oring, Thomas Peternell. "A contraction theorem for divisors fibering over a curve." arXiv:2409.15993 (2024). https://pith.science/paper/XIV6DOSQ
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,283 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.16 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.28 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

Given a Q-Cartier divisor $S \subset X$ admitting a fibration $S \rightarrow B$ onto a curve we give sufficient conditions for the existence of a bimeromorphic contraction contracting S onto B. As a corollary we recover a contraction result for compact K\"ahler threefolds.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 Given a Q-Cartier divisor $S \subset X$ admitting a fibration $S \rightarrow B$ onto a curve we give sufficient conditions for the existence of a bimeromorphic contraction contracting S onto B. contribution 0.55 0.92 0.88 asserted 0.99
s1 As a corollary we recover a contraction result for compact K\"ahler threefolds. result 0.88 0.90 0.10 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

Given a Q-Cartier divisor $S \subset X$ admitting a fibration $S \rightarrow B$ onto a curve we give sufficient conditions for the existence of a bimeromorphic contraction contracting S onto B. As a corollary we recover a contraction result for compact K\"ahler threefolds.

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