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Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces

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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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Eyal Markman

Algebraic Geometry · Submitted 1 Jun 2004

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

The authors' main claim We find generators for the cohomology ring of M, with integral coefficients.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0406016 (version 3)
Pith IDBYVWWKL4, Pith's permanent record of this paper and its review
CitationEyal Markman. "Integral generators for the cohomology ring of moduli spaces of sheaves over Poisson surfaces." arXiv:math/0406016 (2004). https://pith.science/paper/BYVWWKL4
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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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,196 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.55 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.04 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf E exists over SxM, then its class [E] admits a Kunneth decomposition as a class in the tensor product of the topological K-rings K(S) and K(M). The generators are the Chern classes of the Kunneth factors of [E] in K(M). The general case is similar

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 Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. background 0.99 0.10 0.03 asserted 0.87
s1 We find generators for the cohomology ring of M, with integral coefficients. result 0.68 0.96 0.84 asserted 1.00
s2 When S is simply connected and a universal sheaf E exists over SxM, then its class [E] admits a Kunneth decomposition as a class in the tensor product of the topological K-rings K(S) and K(M). result 0.84 0.65 0.08 asserted 0.99
s3 The generators are the Chern classes of the Kunneth factors of [E] in K(M). result 0.91 0.88 0.51 asserted 1.00
s4 The general case is similar result 0.77 0.63 0.04 asserted 0.96

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

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  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • 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

Let M be a smooth and compact moduli space of stable coherent sheaves on a projective surface S with an effective (or trivial) anti-canonical line bundle. We find generators for the cohomology ring of M, with integral coefficients. When S is simply connected and a universal sheaf E exists over SxM, then its class [E] admits a Kunneth decomposition as a class in the tensor product of the topological K-rings K(S) and K(M). The generators are the Chern classes of the Kunneth factors of [E] in K(M). The general case is similar

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