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Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds

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S. Cynk, C. Meyer

Algebraic Geometry · Submitted 9 Apr 2003

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

The authors' main claim The modularity conjecture is verified for all the rigid examples.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0304121 (version 1)
Pith IDMXXYV6RZ, Pith's permanent record of this paper and its review
CitationC. Meyer, S. Cynk. "Geometry and Arithmetic of certain Double Octic Calabi-Yau Manifolds." arXiv:math/0304121 (2003). https://pith.science/paper/MXXYV6RZ
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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, 4,119 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.05 · mentions code or data availability 0.03.

The abstract, sentence by sentence

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

We study Calabi-Yau manifolds constructed as double covers of ${\mathbb P}^3$ branched along an octic surface. We give a list of 85 examples corresponding to arrangements of eight planes defined over ${\mathbb Q}$. The Hodge numbers are computed for all examples. There are 7 rigid Calabi-Yau manifolds and 14 families with $h^{1,2}=1$. The modularity conjecture is verified for all the rigid examples.

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 Calabi-Yau manifolds constructed as double covers of ${\mathbb P}^3$ branched along an octic surface. contribution 0.91 0.83 0.05 asserted 0.98
s1 We give a list of 85 examples corresponding to arrangements of eight planes defined over ${\mathbb Q}$. contribution 0.83 0.94 0.09 asserted 1.00
s2 The Hodge numbers are computed for all examples. result 0.47 0.94 0.09 asserted 1.00
s3 There are 7 rigid Calabi-Yau manifolds and 14 families with $h^{1,2}=1$. result 1.00 0.89 0.26 asserted 1.00
s4 The modularity conjecture is verified for all the rigid examples. result 0.97 0.88 0.33 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.49 · evidence from proof or derivation 0.54.

What was examined, and what was not

sources read
  • 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

We study Calabi-Yau manifolds constructed as double covers of ${\mathbb P}^3$ branched along an octic surface. We give a list of 85 examples corresponding to arrangements of eight planes defined over ${\mathbb Q}$. The Hodge numbers are computed for all examples. There are 7 rigid Calabi-Yau manifolds and 14 families with $h^{1,2}=1$. The modularity conjecture is verified for all the rigid examples.

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