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Gromov-Witten invariants of Fano threefolds of genera 6 and 8

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Victor Przyjalkowski

Algebraic Geometry · Submitted 13 Oct 2004

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

The authors' main claim The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$.

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arXiv IDmath/0410327 (version 4)
Pith IDCQZ2YPLE, Pith's permanent record of this paper and its review
CitationVictor Przyjalkowski. "Gromov-Witten invariants of Fano threefolds of genera 6 and 8." arXiv:math/0410327 (2004). https://pith.science/paper/CQZ2YPLE
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,610 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.24 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.17 · compares with prior results 0.13 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v4. Results and the main claim are underlined; .

The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$. This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. More precisely, we find counting matrices of prime two-pointed Gromov-Witten invariants for them. For this we use the method that lets us find Gromov-Witten invariants of complete intersections in varieties whose invariants are (partially) known.

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 The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$. contribution 0.92 0.40 0.19 asserted 0.95
s1 This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. background 1.00 0.05 0.16 asserted 0.93
s2 More precisely, we find counting matrices of prime two-pointed Gromov-Witten invariants for them. result 0.77 0.95 0.25 asserted 1.00
s3 For this we use the method that lets us find Gromov-Witten invariants of complete intersections in varieties whose invariants are (partially) known. method 1.00 0.53 0.04 asserted 0.98

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.96.

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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

The aim of this paper is to prove Golyshev's conjecture in the cases of Fano threefolds $V_{10}$ and $V_{14}$. This conjecture states modularity of D3 equations for smooth Fano threefolds with Picard group Z. More precisely, we find counting matrices of prime two-pointed Gromov-Witten invariants for them. For this we use the method that lets us find Gromov-Witten invariants of complete intersections in varieties whose invariants are (partially) known.

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