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Smooth foliations on homogeneous compact K\"ahler manifolds

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Federico Lo Bianco, Jorge Vitorio Pereira

Algebraic Geometry · Submitted 17 Jan 2015

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

The authors' main claim We prove that smooth foliations on rational compact homogeneous manifolds are locally trivial fibrations and classify the smooth foliations with all leaves analytically dense on compact homogeneous K\"ahler manifolds.

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arXiv ID1501.04219 (version 1)
Pith IDLK3ESUJK, Pith's permanent record of this paper and its review
CitationFederico Lo Bianco, Jorge Vitorio Pereira. "Smooth foliations on homogeneous compact K\"ahler manifolds." arXiv:1501.04219 (2015). https://pith.science/paper/LK3ESUJK
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,979 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.19 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We study smooth foliations of arbitrary codimension on homogeneous compact K\"ahler manifolds. We prove that smooth foliations on rational compact homogeneous manifolds are locally trivial fibrations and classify the smooth foliations with all leaves analytically dense on compact homogeneous K\"ahler manifolds. Both results are builded upon a (rough) structure Theorem for smooth foliations on compact homogeneous K\"ahler manifolds obtained by comparison of the foliation and the Borel-Remmert decomposition of the ambient.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We study smooth foliations of arbitrary codimension on homogeneous compact K\"ahler manifolds. contribution 0.72 0.81 0.03 asserted 0.63
s1 We prove that smooth foliations on rational compact homogeneous manifolds are locally trivial fibrations and classify the smooth foliations with all leaves analytically dense on compact homogeneous K\"ahler manifolds. result 0.98 0.96 0.85 asserted 1.00
s2 Both results are builded upon a (rough) structure Theorem for smooth foliations on compact homogeneous K\"ahler manifolds obtained by comparison of the foliation and the Borel-Remmert decomposition of the ambient. method 0.92 0.87 0.10 asserted 0.98

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

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not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
not run
  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

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

We study smooth foliations of arbitrary codimension on homogeneous compact K\"ahler manifolds. We prove that smooth foliations on rational compact homogeneous manifolds are locally trivial fibrations and classify the smooth foliations with all leaves analytically dense on compact homogeneous K\"ahler manifolds. Both results are builded upon a (rough) structure Theorem for smooth foliations on compact homogeneous K\"ahler manifolds obtained by comparison of the foliation and the Borel-Remmert decomposition of the ambient.

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Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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