Pith. Sign in

RECORD

Voisin's Conjecture for Zero--cycles on Calabi--Yau Varieties and their Mirrors

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Gilberto Bini, Robert Laterveer, Gianluca Pacienza

Algebraic Geometry · Submitted 1 Jun 2017

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

The authors' main claim Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)K\"unneth decomposition, we provide a general criterion for Calabi-Yau manifolds of dimension at most $5$ to verify Voisin's conjecture.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1706.00472 (version 1)
Pith IDVNEAN4OP, Pith's permanent record of this paper and its review
CitationGianluca Pacienza, Gilberto Bini, Robert Laterveer. "Voisin's Conjecture for Zero--cycles on Calabi--Yau Varieties and their Mirrors." arXiv:1706.00472 (2017). https://pith.science/paper/VNEAN4OP
Claim paper

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,020 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.48 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.53 · compares with prior results 0.24 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study a conjecture, due to Voisin, on 0-cycles on varieties with $p_g=1$. Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)K\"unneth decomposition, we provide a general criterion for Calabi-Yau manifolds of dimension at most $5$ to verify Voisin's conjecture. We then check, using in most cases some cohomological computations on the mirror partners, that the criterion can be successfully applied to various examples in each dimension up to $5$.

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 a conjecture, due to Voisin, on 0-cycles on varieties with $p_g=1$. background 0.81 0.72 0.04 asserted 0.72
s1 Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)K\"unneth decomposition, we provide a general criterion for Calabi-Yau manifolds of dimension at most $5$ to verify Voisin's conjecture. contribution 0.79 0.89 0.62 asserted 1.00
s2 We then check, using in most cases some cohomological computations on the mirror partners, that the criterion can be successfully applied to various examples in each dimension up to $5$. result 0.43 0.94 0.23 asserted 0.89

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 0.94.

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 a conjecture, due to Voisin, on 0-cycles on varieties with $p_g=1$. Using Kimura's finite dimensional motives and recent results of Vial's on the refined (Chow-)K\"unneth decomposition, we provide a general criterion for Calabi-Yau manifolds of dimension at most $5$ to verify Voisin's conjecture. We then check, using in most cases some cohomological computations on the mirror partners, that the criterion can be successfully applied to various examples in each dimension up to $5$.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper cite this in 1 sentence

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

Papers citing it

Cites it as background 1 paper

What it cites · 7 sentences without a confident label

Cites as background 1 paper
  • It is a (somewhat embarrassing) fact that all examples known so far of finite-dimensional motives happen to be in the tensor subcategory generated by Chow motives of curves (i.e., they are “motives of abelian type” in the sense of [ref] ).

    Remarks on motives of abelian type · Finite–dimensional motives · 0.90

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.