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Second variation of Zhang's lambda-invariant on the moduli space of curves

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Robin de Jong

Algebraic Geometry · Submitted 8 Feb 2010

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

The authors' main claim As a result we prove that (8g+4)\lambda is equal, up to a constant, to the \beta-invariant introduced some time ago by R. Hain and D. Reed.

how it is stated · asserted 1.00 read the record →

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arXiv ID1002.1618 (version 2)
Pith IDHJOIVIVK, Pith's permanent record of this paper and its review
CitationRobin de Jong. "Second variation of Zhang's lambda-invariant on the moduli space of curves." arXiv:1002.1618 (2010). https://pith.science/paper/HJOIVIVK
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The compiled record

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,625 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.78 · compares with prior results 0.91 · 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 second variation of the \lambda-invariant, recently introduced by S. Zhang, on the complex moduli space M_g of curves of genus g>1, using work of N. Kawazumi. As a result we prove that (8g+4)\lambda is equal, up to a constant, to the \beta-invariant introduced some time ago by R. Hain and D. Reed. We deduce some consequences; for example we calculate the \lambda-invariant for each hyperelliptic curve, expressing it in terms of the Petersson norm of the discriminant modular form.

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 second variation of the \lambda-invariant, recently introduced by S. contribution 1.00 0.91 0.05 asserted 0.96
s1 Zhang, on the complex moduli space M_g of curves of genus g>1, using work of N. Kawazumi. contribution 0.50 0.48 0.04 asserted 0.77
s2 As a result we prove that (8g+4)\lambda is equal, up to a constant, to the \beta-invariant introduced some time ago by R. Hain and D. Reed. result 1.00 0.87 0.82 asserted 1.00
s3 We deduce some consequences; for example we calculate the \lambda-invariant for each hyperelliptic curve, expressing it in terms of the Petersson norm of the discriminant modular form. result 0.92 0.94 0.10 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · 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
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  • 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 second variation of the \lambda-invariant, recently introduced by S. Zhang, on the complex moduli space M_g of curves of genus g>1, using work of N. Kawazumi. As a result we prove that (8g+4)\lambda is equal, up to a constant, to the \beta-invariant introduced some time ago by R. Hain and D. Reed. We deduce some consequences; for example we calculate the \lambda-invariant for each hyperelliptic curve, expressing it in terms of the Petersson norm of the discriminant modular form.

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References
How the literature uses it

3 arXiv papers cite this in 8 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 · 7 sentences without a confident label

Cites it as support 1 paper
  • It follows rather directly from [ref] (archimedean case) and [ref] (non-archimedean case) that Conjecture [ref] is in fact true.

    Symmetric roots and admissible pairing · Connection with Zhang's $φ$-invariant · 1.00

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