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On K-Stability of Reductive Varieties

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Valery Alexeev, Ludmil Katzarkov

Differential Geometry · Submitted 26 Nov 2003

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

The authors' main claim In this paper we extend Donaldson's results and computations to a new case, that of reductive varieties.

how it is stated · asserted 0.99 read the record →

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arXiv IDmath/0311491 (version 2)
Pith IDAWT5X6H4, Pith's permanent record of this paper and its review
CitationLudmil Katzarkov, Valery Alexeev. "On K-Stability of Reductive Varieties." arXiv:math/0311491 (2003). https://pith.science/paper/AWT5X6H4
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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, 4,095 input tokens.

What the abstract itself states, as probabilities: claims first 0.13 · states limitation 0.17 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.03 · compares with prior results 0.89 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don02] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson's results and computations to a new case, that of reductive varieties. The changes in the second version are cosmetic.

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 G. Tian and S.K. background 0.99 0.03 0.01 unclear 1.00
s1 Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. background 1.00 0.03 0.04 asserted 0.88
s2 In [Don02] Donaldson partially confirmed it in the case of projective toric varieties. background 1.00 0.04 0.03 asserted 0.99
s3 In this paper we extend Donaldson's results and computations to a new case, that of reductive varieties. contribution 1.00 0.90 0.50 asserted 0.99
s4 The changes in the second version are cosmetic. background 0.41 0.52 0.02 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.94.

What was examined, and what was not

sources read
  • arXiv listing abstract v2
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

G. Tian and S.K. Donaldson formulated a conjecture relating GIT stability of a polarized algebraic variety to the existence of a Kahler metric of constant scalar curvature. In [Don02] Donaldson partially confirmed it in the case of projective toric varieties. In this paper we extend Donaldson's results and computations to a new case, that of reductive varieties. The changes in the second version are cosmetic.

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