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Universality of Rank 6 Plucker Relations and Grassmann Cone Preserving Maps

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Alex Kasman, Kathryn Pedings, Amy Reiszl, Takahiro Shiota

Algebraic Geometry · Submitted 5 Oct 2005

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

The authors' main claim We give another finite set of quadratic equations which defines the same embedding, and whose elements all have rank 6.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0510093 (version 3)
Pith IDA5QJNLHT, Pith's permanent record of this paper and its review
CitationAlex Kasman, Amy Reiszl, Kathryn Pedings, Takahiro Shiota. "Universality of Rank 6 Plucker Relations and Grassmann Cone Preserving Maps." arXiv:math/0510093 (2005). https://pith.science/paper/A5QJNLHT
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,566 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.11 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.70 · compares with prior results 0.23 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; .

The Plucker relations define a projective embedding of the Grassmann variety Gr(k,n). We give another finite set of quadratic equations which defines the same embedding, and whose elements all have rank 6. This is achieved by constructing a certain finite set of linear maps from the pth exterior power of n-dimensional space to the 2nd exterior power of 4-dimensional space and pulling back the unique Plucker relation on the latter. We also give a quadratic equation depending on (p+2) parameters having the same properties.

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 Plucker relations define a projective embedding of the Grassmann variety Gr(k,n). background 1.00 0.05 0.05 asserted 1.00
s1 We give another finite set of quadratic equations which defines the same embedding, and whose elements all have rank 6. contribution 0.76 0.96 0.68 asserted 1.00
s2 This is achieved by constructing a certain finite set of linear maps from the pth exterior power of n-dimensional space to the 2nd exterior power of 4-dimensional space and pulling back the unique Plucker relation on the latter. method 1.00 0.94 0.15 asserted 1.00
s3 We also give a quadratic equation depending on (p+2) parameters having the same properties. contribution 0.61 0.94 0.16 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from proof or derivation 1.00.

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  • figures and tables
  • 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

The Plucker relations define a projective embedding of the Grassmann variety Gr(k,n). We give another finite set of quadratic equations which defines the same embedding, and whose elements all have rank 6. This is achieved by constructing a certain finite set of linear maps from the pth exterior power of n-dimensional space to the 2nd exterior power of 4-dimensional space and pulling back the unique Plucker relation on the latter. We also give a quadratic equation depending on (p+2) parameters having the same properties.

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2 arXiv papers cite this in 4 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

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