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On deformations of Q-Fano threefolds

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Taro Sano

Algebraic Geometry · Submitted 28 Mar 2012

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

The authors' main claim Second, we show that every Q-Fano 3-fold with only "ordinary" terminal singularities is Q-smoothable, that is, it can be deformed to a Q-Fano 3-fold with only quotient singularities.

how it is stated · asserted 1.00 read the record →

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arXiv ID1203.6323 (version 6)
Pith IDMCVCQLZS, Pith's permanent record of this paper and its review
CitationTaro Sano. "On deformations of Q-Fano threefolds." arXiv:1203.6323 (2012). https://pith.science/paper/MCVCQLZS
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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, 4,254 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.44 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.56 · compares with prior results 0.06 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v6. Results and the main claim are underlined; .

We study the deformation theory of a Q-Fano 3-fold with only terminal singularities. First, we show that the Kuranishi space of a Q-Fano 3-fold is smooth. Second, we show that every Q-Fano 3-fold with only "ordinary" terminal singularities is Q-smoothable, that is, it can be deformed to a Q-Fano 3-fold with only quotient singularities. Finally, we prove Q-smoothability of a Q-Fano 3-fold assuming the existence of a Du Val anticanonical element. As an application, we get the genus bound for primary Q-Fano 3-folds with Du Val anticanonical elements.

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 the deformation theory of a Q-Fano 3-fold with only terminal singularities. contribution 0.83 0.86 0.06 asserted 0.68
s1 First, we show that the Kuranishi space of a Q-Fano 3-fold is smooth. result 0.99 0.94 0.17 asserted 1.00
s2 Second, we show that every Q-Fano 3-fold with only "ordinary" terminal singularities is Q-smoothable, that is, it can be deformed to a Q-Fano 3-fold with only quotient singularities. result 0.97 0.93 0.28 asserted 1.00
s3 Finally, we prove Q-smoothability of a Q-Fano 3-fold assuming the existence of a Du Val anticanonical element. result 0.95 0.94 0.19 asserted 1.00
s4 As an application, we get the genus bound for primary Q-Fano 3-folds with Du Val anticanonical elements. result 0.93 0.94 0.13 asserted 1.00

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

What was examined, and what was not

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  • arXiv listing abstract v6
not examined
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  • references and citing sentences
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  • P abstract
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  • 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 the deformation theory of a Q-Fano 3-fold with only terminal singularities. First, we show that the Kuranishi space of a Q-Fano 3-fold is smooth. Second, we show that every Q-Fano 3-fold with only "ordinary" terminal singularities is Q-smoothable, that is, it can be deformed to a Q-Fano 3-fold with only quotient singularities. Finally, we prove Q-smoothability of a Q-Fano 3-fold assuming the existence of a Du Val anticanonical element. As an application, we get the genus bound for primary Q-Fano 3-folds with Du Val anticanonical elements.

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How the literature uses it

2 arXiv papers cite this in 19 sentences

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 · 11 sentences without a confident label

Builds on it 1 paper
Uses its method or tool 1 paper
Cites it as background 1 paper
  • The author studied a deformation of a $ℚ$-Fano $3$-fold with its anticanonical element in [ref] and [ref] .

    On deformations of Q-Fano threefolds II · $ℚ$-smoothing of $ℚ$-Fano $3$-folds · 0.88

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