Pith. Sign in

RECORD

Picard-Fuchs system for family of Kummer surfaces as subsystem of GKZ hypergeometric system

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
Atsuhira Nagano

Algebraic Geometry · Submitted 26 Aug 2024

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

The authors' main claim We determine a simple expression of the Picard-Fuchs system for a family of Kummer surfaces for all principally polarized Abelian surfaces.

how it is stated · asserted 1.00 read the record →

Comment (0) Read on arXiv ↗
Cite ▾
arXiv ID2408.14271 (version 2)
Pith ID2LYGM7KG, Pith's permanent record of this paper and its review
CitationAtsuhira Nagano. "Picard-Fuchs system for family of Kummer surfaces as subsystem of GKZ hypergeometric system." arXiv:2408.14271 (2024). https://pith.science/paper/2LYGM7KG
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, 2,914 input tokens.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.91 · compares with prior results 0.07 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We determine a simple expression of the Picard-Fuchs system for a family of Kummer surfaces for all principally polarized Abelian surfaces. It is given by a system of linear partial differential equations in three variables of rank five. Our results are based on a Jacobian elliptic fibration on Kummer surfaces and a GKZ hypergeometric system suited to the elliptic fibration.

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 determine a simple expression of the Picard-Fuchs system for a family of Kummer surfaces for all principally polarized Abelian surfaces. contribution 0.50 0.95 0.87 asserted 1.00
s1 It is given by a system of linear partial differential equations in three variables of rank five. result 0.98 0.82 0.19 asserted 1.00
s2 Our results are based on a Jacobian elliptic fibration on Kummer surfaces and a GKZ hypergeometric system suited to the elliptic fibration. method 1.00 0.76 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
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 determine a simple expression of the Picard-Fuchs system for a family of Kummer surfaces for all principally polarized Abelian surfaces. It is given by a system of linear partial differential equations in three variables of rank five. Our results are based on a Jacobian elliptic fibration on Kummer surfaces and a GKZ hypergeometric system suited to the elliptic fibration.

Human review

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

References

Discussion

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