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Deformations of cones of primitive vectors

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Sebastien Jansou

Algebraic Geometry · Submitted 8 Jun 2005

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

The authors' main claim For a complex connected reductive group G, we classify the simple modules whose cone of primitive vectors admits a nontrivial G-invariant deformation.

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arXiv IDmath/0506133 (version 2)
Pith ID3OCFJ3PN, Pith's permanent record of this paper and its review
CitationSebastien Jansou. "Deformations of cones of primitive vectors." arXiv:math/0506133 (2005). https://pith.science/paper/3OCFJ3PN
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,656 input tokens.

What the abstract itself states, as probabilities: claims first 0.64 · states limitation 0.58 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.83 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

For a complex connected reductive group G, we classify the simple modules whose cone of primitive vectors admits a nontrivial G-invariant deformation. We relate this classification to that of simple Jordan algebras, and to that (due to Akhiezer) of smooth projective varieties whose orbits under the action of a connected affine algebraic group are a divisor and its complementary. Our main tool is the invariant Hilbert scheme of Alexeev-Brion; we determine the first examples of it. We also determine the infinitesimal deformations (non necessarily G-invariant) of the cones of primitive vectors; they turn out to be trivial for most simple modules.

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 For a complex connected reductive group G, we classify the simple modules whose cone of primitive vectors admits a nontrivial G-invariant deformation. contribution 0.58 0.95 0.74 asserted 1.00
s1 We relate this classification to that of simple Jordan algebras, and to that (due to Akhiezer) of smooth projective varieties whose orbits under the action of a connected affine algebraic group are a divisor and its complementary. interpretation 0.47 0.76 0.14 asserted 1.00
s2 Our main tool is the invariant Hilbert scheme of Alexeev-Brion; we determine the first examples of it. method 0.77 0.94 0.11 asserted 1.00
s3 We also determine the infinitesimal deformations (non necessarily G-invariant) of the cones of primitive vectors; they turn out to be trivial for most simple modules. result 0.95 0.95 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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  • references and citing sentences
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  • 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

For a complex connected reductive group G, we classify the simple modules whose cone of primitive vectors admits a nontrivial G-invariant deformation. We relate this classification to that of simple Jordan algebras, and to that (due to Akhiezer) of smooth projective varieties whose orbits under the action of a connected affine algebraic group are a divisor and its complementary. Our main tool is the invariant Hilbert scheme of Alexeev-Brion; we determine the first examples of it. We also determine the infinitesimal deformations (non necessarily G-invariant) of the cones of primitive vectors; they turn out to be trivial for most simple modules.

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