Pith. Sign in

RECORD

Donaldson-Thomas invariants of local elliptic surfaces via the topological vertex

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
Jim Bryan, Martijn Kool

Algebraic Geometry · Submitted 26 Aug 2016

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

The authors' main claim We compute the Donaldson-Thomas invariants of a local elliptic surface with section.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID1608.07369 (version 2)
Pith ID4XTPTXQU, Pith's permanent record of this paper and its review
CitationJim Bryan, Martijn Kool. "Donaldson-Thomas invariants of local elliptic surfaces via the topological vertex." arXiv:1608.07369 (2016). https://pith.science/paper/4XTPTXQU
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, 4,862 input tokens.

What the abstract itself states, as probabilities: claims first 0.07 · states limitation 0.09 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.09 · compares with prior results 0.85 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We compute the Donaldson-Thomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the invariants in terms of the topological vertex. Utilizing identities for the topological vertex proved in arXiv:1603.05271, we derive product formulas for the partition functions. The connected version of the partition function is written in terms of Jacobi forms. In the special case where the elliptic surface is a K3 surface, we get a derivation of the Katz-Klemm-Vafa formula for primitive curve classes which is independent of the computation of Kawai-Yoshioka.

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 compute the Donaldson-Thomas invariants of a local elliptic surface with section. contribution 0.59 0.95 0.66 asserted 1.00
s1 We introduce a new computational technique which is a mixture of motivic and toric methods. method 0.66 0.94 0.06 asserted 1.00
s2 This allows us to write the partition function for the invariants in terms of the topological vertex. result 0.38 0.92 0.15 asserted 0.99
s3 Utilizing identities for the topological vertex proved in arXiv:1603.05271, we derive product formulas for the partition functions. result 0.51 0.86 0.12 asserted 1.00
s4 The connected version of the partition function is written in terms of Jacobi forms. result 0.98 0.90 0.11 asserted 1.00
s5 In the special case where the elliptic surface is a K3 surface, we get a derivation of the Katz-Klemm-Vafa formula for primitive curve classes which is independent of the computation of Kawai-Yoshioka. result 0.93 0.92 0.30 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.67 · evidence from proof or derivation 1.00.

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
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 compute the Donaldson-Thomas invariants of a local elliptic surface with section. We introduce a new computational technique which is a mixture of motivic and toric methods. This allows us to write the partition function for the invariants in terms of the topological vertex. Utilizing identities for the topological vertex proved in arXiv:1603.05271, we derive product formulas for the partition functions. The connected version of the partition function is written in terms of Jacobi forms. In the special case where the elliptic surface is a K3 surface, we get a derivation of the Katz-Klemm-Vafa formula for primitive curve classes which is independent of the computation of Kawai-Yoshioka.

Human review

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

How the literature uses it

6 arXiv papers cite this in 7 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 · 4 sentences without a confident label

Uses its method or tool 1 paper
Compares with it 1 paper
Cites it as background 1 paper

What it cites · 4 sentences without a confident label

Uses the method or tool of 1 paper
  • Substituting the values of $F_1$, $F_2$, $g$, and $h$ from Proposition [ref] into Corollary [ref]F2^e(S)(sum g q^a)^e(B)-e(S)..., and then substituting in the formulas from Lemma [ref] we obtain the following [equation] From the Okounkov-Reshitikhin-Vafa formula for the topological vertex [ref] , [ref] we get [equation] which we substitute into the above to find [equation] Applying [ref] , we see that [equation] Noting that $e(B)$ is even, the above expression is easily seen to be equivalent to the formula for $(X)$ in Theorem [ref].

    Quantum Calabi-Yau and Classical Crystals · Applying the trace formulas · 0.93

Cites as support 1 paper
  • This follows from the computations in [ref] .

    math.AG/0312059 · Including the Behrend function · 0.97

Discussion

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