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Conic bundles and Clifford algebras

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Daniel Chan, Colin Ingalls

Rings and Algebras · Submitted 10 Jan 2011

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

The authors' main claim We use the even Clifford algebra, and the Brauer-Severi Variety, and other constructions to give natural bijections between these objects under appropriate hypothesis.

how it is stated · asserted 1.00 read the record →

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arXiv ID1101.1705 (version 1)
Pith IDWMDLDOIC, Pith's permanent record of this paper and its review
CitationColin Ingalls, Daniel Chan. "Conic bundles and Clifford algebras." arXiv:1101.1705 (2011). https://pith.science/paper/WMDLDOIC
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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, 3,575 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.37 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.05 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

We discuss natural connections between three objects: quadratic forms with values in line bundles, conic bundles and quaternion orders. We use the even Clifford algebra, and the Brauer-Severi Variety, and other constructions to give natural bijections between these objects under appropriate hypothesis. We then restrict to a surface base and we express the second Chern class of the order in terms $K^3$ and other invariants of the corresponding conic bundle. We find the conic bundles corresponding to minimal del Pezzo quaterion orders and we discuss problems concerning their moduli.

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 discuss natural connections between three objects: quadratic forms with values in line bundles, conic bundles and quaternion orders. contribution 0.79 0.71 0.15 asserted 0.96
s1 We use the even Clifford algebra, and the Brauer-Severi Variety, and other constructions to give natural bijections between these objects under appropriate hypothesis. method 0.83 0.93 0.46 asserted 1.00
s2 We then restrict to a surface base and we express the second Chern class of the order in terms $K^3$ and other invariants of the corresponding conic bundle. result 0.78 0.93 0.14 asserted 1.00
s3 We find the conic bundles corresponding to minimal del Pezzo quaterion orders and we discuss problems concerning their moduli. contribution 0.77 0.94 0.20 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 v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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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 discuss natural connections between three objects: quadratic forms with values in line bundles, conic bundles and quaternion orders. We use the even Clifford algebra, and the Brauer-Severi Variety, and other constructions to give natural bijections between these objects under appropriate hypothesis. We then restrict to a surface base and we express the second Chern class of the order in terms $K^3$ and other invariants of the corresponding conic bundle. We find the conic bundles corresponding to minimal del Pezzo quaterion orders and we discuss problems concerning their moduli.

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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

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