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Momentum polytopes of projective spherical varieties and related K\"ahler geometry

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Stéphanie Cupit-Foutou, Guido Pezzini, Bart Van Steirteghem

Algebraic Geometry · Submitted 21 Sep 2018

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

The authors' main claim This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties.

how it is stated · asserted 1.00 read the record →

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arXiv ID1809.08171 (version 3)
Pith IDD32JA2EN, Pith's permanent record of this paper and its review
CitationBart Van Steirteghem, Guido Pezzini, St\'ephanie Cupit-Foutou. "Momentum polytopes of projective spherical varieties and related K\"ahler geometry." arXiv:1809.08171 (2018). https://pith.science/paper/D32JA2EN
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,019 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.12 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.06 · mentions code or data availability 0.02.

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

We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties. In the setting of multiplicity free compact and connected Hamiltonian manifolds, we obtain a necessary and sufficient condition involving momentum polytopes for such manifolds to be K\"ahler and classify the invariant compatible complex structures of a given K\"ahler multiplicity free compact and connected Hamiltonian manifold.

background contribution method result interpretation main claim

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 We apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. contribution 0.88 0.94 0.29 asserted 1.00
s1 This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties. result 0.96 0.94 0.38 asserted 1.00
s2 In the setting of multiplicity free compact and connected Hamiltonian manifolds, we obtain a necessary and sufficient condition involving momentum polytopes for such manifolds to be K\"ahler and classify the invariant compatible complex structures of a given K\"ahler multiplicity free compact and connected Hamiltonian manifold. result 0.86 0.92 0.24 asserted 1.00

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

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  • C citations
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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 apply the combinatorial theory of spherical varieties to characterize the momentum polytopes of polarized projective spherical varieties. This enables us to derive a classification of these varieties, without specifying the open orbit, as well as a classification of all Fano spherical varieties. In the setting of multiplicity free compact and connected Hamiltonian manifolds, we obtain a necessary and sufficient condition involving momentum polytopes for such manifolds to be K\"ahler and classify the invariant compatible complex structures of a given K\"ahler multiplicity free compact and connected Hamiltonian manifold.

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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

What it cites

Uses the method or tool of 1 paper
  • We use the classification of spherical homogeneous spaces [ref] via homogeneous spherical data, which were introduced by Luna in [ref] (see [ref] for a compact definition).

    Wonderful Varieties: A geometrical realization · Existence of Kaehler structures: sufficiency · 0.89

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