Pith. Sign in

RECORD

An investigation of stability on certain toric surfaces

PaperPDF from arXiv

data files

Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
X Bluesky LinkedIn Reddit Hacker News
Lars Martin Sektnan

Differential Geometry · Submitted 28 Oct 2016

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

The authors' main claim This in turn implies the existence of a definite log-stable region for generic quadrilaterals.

how it is stated · asserted 0.99 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1610.09419 (version 1)
Pith ID35XTAX5O, Pith's permanent record of this paper and its review
CitationLars Martin Sektnan. "An investigation of stability on certain toric surfaces." arXiv:1610.09419 (2016). https://pith.science/paper/35XTAX5O
Claim paper

The compiled record

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.

Open the compiled record

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,851 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.21 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.11 · compares with prior results 0.15 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We investigate the relationship between stability and the existence of extremal K\"ahler metrics on certain toric surfaces. In particular, we consider how log stability depends on weights for toric surfaces whose moment polytope is a quadrilateral. We introduce a space of symplectic potentials for toric manifolds, which induces metrics with mixed Poincar\'e type and cone angle singularities. For quadrilaterals, we give a computable criterion for stability with 0 weights along two of the edges of the quadrilateral. This in turn implies the existence of a definite log-stable region for generic quadrilaterals. This uses constructions due to Apostolov-Calderbank-Gauduchon and Legendre.

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 We investigate the relationship between stability and the existence of extremal K\"ahler metrics on certain toric surfaces. contribution 0.78 0.90 0.07 asserted 0.60
s1 In particular, we consider how log stability depends on weights for toric surfaces whose moment polytope is a quadrilateral. contribution 0.93 0.81 0.06 asserted 0.82
s2 We introduce a space of symplectic potentials for toric manifolds, which induces metrics with mixed Poincar\'e type and cone angle singularities. contribution 0.62 0.90 0.04 asserted 1.00
s3 For quadrilaterals, we give a computable criterion for stability with 0 weights along two of the edges of the quadrilateral. result 0.73 0.95 0.22 asserted 1.00
s4 This in turn implies the existence of a definite log-stable region for generic quadrilaterals. interpretation 0.57 0.87 0.40 asserted 0.99
s5 This uses constructions due to Apostolov-Calderbank-Gauduchon and Legendre. method 0.77 0.05 0.03 asserted 0.96

What kind of paper the classifier reports this is: theoretical result 0.97 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
levels run
  • P abstract
not run
  • 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

We investigate the relationship between stability and the existence of extremal K\"ahler metrics on certain toric surfaces. In particular, we consider how log stability depends on weights for toric surfaces whose moment polytope is a quadrilateral. We introduce a space of symplectic potentials for toric manifolds, which induces metrics with mixed Poincar\'e type and cone angle singularities. For quadrilaterals, we give a computable criterion for stability with 0 weights along two of the edges of the quadrilateral. This in turn implies the existence of a definite log-stable region for generic quadrilaterals. This uses constructions due to Apostolov-Calderbank-Gauduchon and Legendre.

Human review

How Pith checks papers → · Full audit of this paper →

How the literature uses it

1 arXiv paper 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

Papers citing it · 2 sentences without a confident label

Uses its method or tool 1 paper

Discussion

Know something about this paper? Leave a comment, or highlight any passage above to comment on it.