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Newton-Okounkov bodies on projective bundles over curves

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Pedro Montero

Algebraic Geometry · Submitted 20 Mar 2017

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

The authors' main claim Moreover, we characterize semi-stable vector bundles over curves via Newton-Okounkov bodies.

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arXiv ID1703.06828 (version 3)
Pith IDA4576R7K, Pith's permanent record of this paper and its review
CitationPedro Montero. "Newton-Okounkov bodies on projective bundles over curves." arXiv:1703.06828 (2017). https://pith.science/paper/A4576R7K
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,872 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.25 · mentions code or data availability 0.02.

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

In this article, we study Newton-Okounkov bodies on projective vector bundles over curves. Inspired by Wolfe's estimates used to compute the volume function on these varieties, we compute all Newton-Okounkov bodies with respect to linear flags. Moreover, we characterize semi-stable vector bundles over curves via Newton-Okounkov bodies.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 In this article, we study Newton-Okounkov bodies on projective vector bundles over curves. contribution 0.81 0.84 0.07 asserted 0.89
s1 Inspired by Wolfe's estimates used to compute the volume function on these varieties, we compute all Newton-Okounkov bodies with respect to linear flags. contribution 0.54 0.92 0.18 asserted 1.00
s2 Moreover, we characterize semi-stable vector bundles over curves via Newton-Okounkov bodies. result 0.90 0.93 0.44 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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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

In this article, we study Newton-Okounkov bodies on projective vector bundles over curves. Inspired by Wolfe's estimates used to compute the volume function on these varieties, we compute all Newton-Okounkov bodies with respect to linear flags. Moreover, we characterize semi-stable vector bundles over curves via Newton-Okounkov bodies.

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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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Cites as support 1 paper
  • We notice that if for all linear flags $Y_∙$ the Newton-Okounkov body of $η=a(ξ-μ_ℓf)+bf$ is given by $Δ_Y_∙(η)=[0,b]×aΔ_r-1 ⊆ℝ^r$ then $η$ is a big and nef class, by [ref] .

    Positivity of line bundles and Newton-Okounkov bodies · Some reductions · 0.99

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