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Almost complex manifolds from the point of view of Kodaira dimension

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Andrea Cattaneo

Complex Variables · Submitted 26 Jul 2023

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

The authors' main claim At the end we conclude with some speculations on the theory of meromorphic functions on almost complex manifolds.

how it is stated · speculative 0.87 read the record →

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arXiv ID2307.14215 (version 1)
Pith IDVKUKUBGV, Pith's permanent record of this paper and its review
CitationAndrea Cattaneo. "Almost complex manifolds from the point of view of Kodaira dimension." arXiv:2307.14215 (2023). https://pith.science/paper/VKUKUBGV
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,697 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.18 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.35 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira dimension is invariant under holomorphic deformations for a smooth projective manifolds, while there are examples of holomorphic deformations of non-projective manifolds for which the Kodaira dimension is non-constant. Recently this concept has been generalized to almost complex manifolds, we want to present here some of its main features in the non-integrable case, mainly with respect to deformations. At the end we conclude with some speculations on the theory of meromorphic functions on almost complex manifolds.

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 In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. background 1.00 0.03 0.02 asserted 1.00
s1 Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira dimension is invariant under holomorphic deformations for a smooth projective manifolds, while there are examples of holomorphic deformations of non-projective manifolds for which the Kodaira dimension is non-constant. background 1.00 0.03 0.04 asserted 1.00
s2 Recently this concept has been generalized to almost complex manifolds, we want to present here some of its main features in the non-integrable case, mainly with respect to deformations. contribution 0.94 0.22 0.09 asserted 0.93
s3 At the end we conclude with some speculations on the theory of meromorphic functions on almost complex manifolds. future work 0.96 0.55 0.22 speculative 0.87

What kind of paper the classifier reports this is: review 0.96 · evidence from literature 0.58.

What was examined, and what was not

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  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • 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

In complex geometry a classical and useful invariant of a complex manifold is its Kodaira dimension. Since its introduction by Iitaka in the early 70's, its behavior under deformations was object of study and it is known that Kodaira dimension is invariant under holomorphic deformations for a smooth projective manifolds, while there are examples of holomorphic deformations of non-projective manifolds for which the Kodaira dimension is non-constant. Recently this concept has been generalized to almost complex manifolds, we want to present here some of its main features in the non-integrable case, mainly with respect to deformations. At the end we conclude with some speculations on the theory of meromorphic functions on almost complex manifolds.

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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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