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Genus of curves in generic hypersurfaces

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Bin Wang

Algebraic Geometry · Submitted 2 Oct 2011

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

The authors' main claim In particular, there are no smooth elliptic curves in generic hypersurfaces of degree $$h\geq 2n-1.$$ This application in return leads to a study of the deformation of the pair mentioned above.

how it is stated · asserted 1.00 read the record →

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arXiv ID1110.0185 (version 3)
Pith IDVF7V6UIF, Pith's permanent record of this paper and its review
CitationBin Wang. "Genus of curves in generic hypersurfaces." arXiv:1110.0185 (2011). https://pith.science/paper/VF7V6UIF
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-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,351 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.23 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.95 · compares with prior results 0.52 · mentions code or data availability 0.01.

The abstract, sentence by sentence

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

This is the continuation of our paper [10]. In this paper which is self contained, we would like to give a different obstruction formula to the FIRST order deformation of the pair of a smooth curve and a smooth hypersurface. This obstruction formula leads to a genus formula for a smooth curve in a smooth hypersurface. As an application we show that smooth elliptic curves in a smooth hypersurface of degree $$h\geq 2n-1$$ in the projective space $\mathbf P^n, n\geq 3,$ can't deform in the first order to all hypersurfaces of the same degree. In particular, there are no smooth elliptic curves in generic hypersurfaces of degree $$h\geq 2n-1.$$ This application in return leads to a study of the deformation of the pair mentioned above.

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 This is the continuation of our paper [10]. background 1.00 0.16 0.01 asserted 0.98
s1 In this paper which is self contained, we would like to give a different obstruction formula to the FIRST order deformation of the pair of a smooth curve and a smooth hypersurface. contribution 1.00 0.79 0.08 asserted 0.64
s2 This obstruction formula leads to a genus formula for a smooth curve in a smooth hypersurface. result 0.88 0.90 0.31 asserted 0.99
s3 As an application we show that smooth elliptic curves in a smooth hypersurface of degree $$h\geq 2n-1$$ in the projective space $\mathbf P^n, n\geq 3,$ can't deform in the first order to all hypersurfaces of the same degree. result 0.99 0.93 0.29 asserted 1.00
s4 In particular, there are no smooth elliptic curves in generic hypersurfaces of degree $$h\geq 2n-1.$$ This application in return leads to a study of the deformation of the pair mentioned above. result 0.96 0.89 0.34 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v3
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

This is the continuation of our paper [10]. In this paper which is self contained, we would like to give a different obstruction formula to the FIRST order deformation of the pair of a smooth curve and a smooth hypersurface. This obstruction formula leads to a genus formula for a smooth curve in a smooth hypersurface. As an application we show that smooth elliptic curves in a smooth hypersurface of degree $$h\geq 2n-1$$ in the projective space $\mathbf P^n, n\geq 3,$ can't deform in the first order to all hypersurfaces of the same degree. In particular, there are no smooth elliptic curves in generic hypersurfaces of degree $$h\geq 2n-1.$$ This application in return leads to a study of the deformation of the pair mentioned above.

Human review

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How the literature uses it

2 arXiv papers cite this in 2 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

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