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Classification of K3-surfaces with involution and maximal symplectic symmetry

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Kristina Frantzen

Algebraic Geometry · Submitted 10 Jun 2009

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

The authors' main claim A complete classification of K3-surfaces with maximal symplectic symmetry is obtained.

how it is stated · asserted 1.00 read the record →

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arXiv ID0906.1867 (version 1)
Pith IDCM5Z5KJA, Pith's permanent record of this paper and its review
CitationKristina Frantzen. "Classification of K3-surfaces with involution and maximal symplectic symmetry." arXiv:0906.1867 (2009). https://pith.science/paper/CM5Z5KJA
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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, 2,876 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.07 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

K3-surfaces with antisymplectic involution and compatible symplectic actions of finite groups are considered. In this situation actions of large finite groups of symplectic transformations are shown to arise via double covers of Del Pezzo surfaces. A complete classification of K3-surfaces with maximal symplectic symmetry is obtained.

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 K3-surfaces with antisymplectic involution and compatible symplectic actions of finite groups are considered. background 0.80 0.40 0.04 asserted 0.69
s1 In this situation actions of large finite groups of symplectic transformations are shown to arise via double covers of Del Pezzo surfaces. result 0.90 0.85 0.13 asserted 1.00
s2 A complete classification of K3-surfaces with maximal symplectic symmetry is obtained. result 0.87 0.93 0.90 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

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

K3-surfaces with antisymplectic involution and compatible symplectic actions of finite groups are considered. In this situation actions of large finite groups of symplectic transformations are shown to arise via double covers of Del Pezzo surfaces. A complete classification of K3-surfaces with maximal symplectic symmetry is obtained.

Human review

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What this paper does with the arXiv papers it cites

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

What it cites · 8 sentences without a confident label

Cites as background 3 papers
  • Initiated by Bayle and Beauville in [ref] , the methods have been employed in the classification of subgroups of the Cremona group $Bir(ℙ_2)$ for example by Beauville and Blanc ( [ref] , [ref] , [ref] [ref] ), de Fernex [ref] , Dolgachev and Iskovskikh [ref] , [ref] , and Zhang [ref] .

    On elements of prime order in the plane Cremona group over a perfect field · Equivariant minimal model program · 0.83

  • Initiated by Bayle and Beauville in [ref] , the methods have been employed in the classification of subgroups of the Cremona group $Bir(ℙ_2)$ for example by Beauville and Blanc ( [ref] , [ref] , [ref] [ref] ), de Fernex [ref] , Dolgachev and Iskovskikh [ref] , [ref] , and Zhang [ref] .

    Finite subgroups of the plane Cremona group · Equivariant minimal model program · 0.83

  • Initiated by Bayle and Beauville in [ref] , the methods have been employed in the classification of subgroups of the Cremona group $Bir(ℙ_2)$ for example by Beauville and Blanc ( [ref] , [ref] , [ref] [ref] ), de Fernex [ref] , Dolgachev and Iskovskikh [ref] , [ref] , and Zhang [ref] .

    math.AG/0610368 · Equivariant minimal model program · 0.83

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