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The 2-leg vertex in K-theoretic DT theory

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Ya. Kononov, A. Okounkov, A. Osinenko

Mathematical Physics · Submitted 4 May 2019

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

The authors' main claim In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial.

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arXiv ID1905.01523 (version 1)
Pith IDMWVKAWML, Pith's permanent record of this paper and its review
CitationA. Okounkov, A. Osinenko, Ya. Kononov. "The 2-leg vertex in K-theoretic DT theory." arXiv:1905.01523 (2019). https://pith.science/paper/MWVKAWML
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,898 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.47 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.07 · compares with prior results 0.09 · mentions code or data availability 0.02.

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

K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial. We also discuss some applications of this result.

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#sentencerolethe authors' own workstates the main conclusionstrength
s0 K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. background 1.00 0.10 0.07 asserted 0.90
s1 In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial. contribution 0.68 0.97 0.86 asserted 1.00
s2 We also discuss some applications of this result. contribution 0.96 0.85 0.05 asserted 0.77

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

K-theoretic Donaldson-Thomas counts of curves in toric and many related threefolds can be computed in terms of a certain canonical 3-valent tensor, the K-theoretic equivariant vertex. In this paper we derive a formula for the vertex in the case when two out of three entries are nontrivial. We also discuss some applications of this result.

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9 arXiv papers cite this in 14 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 · 8 sentences without a confident label

Compares with it 1 paper
  • In particular this produces a prediction for the large radius conifold partition function, as Z'_DT (t_4 , t_5 , q_1) = ^∙q_1/(-1/√(t_4)+√(t_4)) (-1/√(t_5)+√(t_5)) which agrees with the result of [ref] , upon the usual change of variables $t_4 = q / √(κ)$ and $t_5 = 1/ (q √(κ))$.

    On the M2-Brane Index on Noncommutative Crepant Resolutions · Refined and unrefined limits · 0.95

Cites it as support 1 paper
  • Therefore[Recall the origin of the minus sign from Theorem [ref].] [equation] Hence Conjecture [ref] implies [equation] This equality was recently proved by Kononov-Okounkov-Osinenko [ref] , which gives good evidence for Conjecture [ref] from our perspective.

    $K$-theoretic DT/PT correspondence for toric Calabi-Yau 4-folds · Local resolved conifold · 0.99

Cites it as background 4 papers

What it cites · 13 sentences without a confident label

Uses the method or tool of 1 paper
Cites as background 3 papers
  • See Chapter 9 in [ref] for an introduction to stable envelopes in equivariant K-theory.

    Lectures on K-theoretic computations in enumerative geometry · Section · 1.00

  • While there is an in principle understanding of the vertices in terms of the Fock space representations of quantum double loop groups (see [ref] for an introduction), having a better handle on them would lead to a significant theoretical and computational progress.

    Takagi lectures on Donaldson-Thomas theory · Section · 0.97

  • See, for example, [ref] for a set of introductory lectures, and also [ref] for an early discussion of the meaning of DT counts in theoretical physics.

    Quantum Foam and Topological Strings · Section · 1.00

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