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Cohomology of the second Voronoi compactification of A_4

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Klaus Hulek, Orsola Tommasi

Algebraic Geometry · Submitted 31 Mar 2011

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

The authors' main claim In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10.

how it is stated · asserted 1.00 read the record →

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arXiv ID1103.6169 (version 2)
Pith IDGCK45IID, Pith's permanent record of this paper and its review
CitationKlaus Hulek, Orsola Tommasi. "Cohomology of the second Voronoi compactification of A_4." arXiv:1103.6169 (2011). https://pith.science/paper/GCK45IID
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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.

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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,955 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.95 · human participants 0.01 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.31 · compares with prior results 0.32 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10. We also compute the cohomology groups of the perfect cone compactification in degree < 10. The main tool is the investigation of the strata of the compactification corresponding to semi-abelic varieties with constant torus rank.

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 In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10. result 0.60 0.97 0.84 asserted 1.00
s1 We also compute the cohomology groups of the perfect cone compactification in degree < 10. result 0.87 0.95 0.09 asserted 1.00
s2 The main tool is the investigation of the strata of the compactification corresponding to semi-abelic varieties with constant torus rank. method 1.00 0.84 0.04 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.98.

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

In this paper we compute the cohomology groups of the second Voronoi compactification of the moduli space of abelian fourfolds in all degrees with the exception of the middle degree 10. We also compute the cohomology groups of the perfect cone compactification in degree < 10. The main tool is the investigation of the strata of the compactification corresponding to semi-abelic varieties with constant torus rank.

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2 arXiv papers cite this in 4 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 · 3 sentences without a confident label

Uses its method or tool 1 paper
  • This idea can be used to try to compute the cohomology of $_g^tor$ inductively, and this is the approach taken in [ref] .

    Geometry of theta divisors --- a survey · Class computations, and intersection theory on $_g$ · 0.88

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