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Generating series in the cohomology of Hilbert schemes of points on surfaces

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Samuel Boissiere, Marc A. Nieper-Wisskirchen

Algebraic Geometry · Submitted 27 Oct 2006

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

The authors' main claim We also explain the algorithmic counterpart of the topic: The cohomology space is governed by a vertex algebra that can be used to compute characteristic classes.

how it is stated · asserted 1.00 read the record →

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arXiv IDmath/0610837 (version 1)
Pith IDWDZERIFU, Pith's permanent record of this paper and its review
CitationMarc A. Nieper-Wisskirchen, Samuel Boissiere. "Generating series in the cohomology of Hilbert schemes of points on surfaces." arXiv:math/0610837 (2006). https://pith.science/paper/WDZERIFU
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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, 4,812 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.08 · human participants 0.01 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.32 · mentions code or data availability 0.14.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

In the study of the rational cohomology of Hilbert schemes of points on a smooth surface, it is particularly interesting to understand the characteristic classes of the tautological bundles and the tangent bundle. In this note we pursue this study. We first collect all results appearing separately in the literature and prove some new formulas using T. Ohmoto's results on orbifold Chern classes on Hilbert schemes. We also explain the algorithmic counterpart of the topic: The cohomology space is governed by a vertex algebra that can be used to compute characteristic classes. We present an implementation of the vertex operators in the rewriting logic system {\sc Maude} and address observations and conjectures obtained after symbolic computations.

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 the study of the rational cohomology of Hilbert schemes of points on a smooth surface, it is particularly interesting to understand the characteristic classes of the tautological bundles and the tangent bundle. background 1.00 0.05 0.05 asserted 0.90
s1 In this note we pursue this study. contribution 0.84 0.47 0.03 asserted 0.74
s2 We first collect all results appearing separately in the literature and prove some new formulas using T. contribution 0.86 0.90 0.07 asserted 0.98
s3 Ohmoto's results on orbifold Chern classes on Hilbert schemes. method 0.44 0.07 0.05 unclear 0.78
s4 We also explain the algorithmic counterpart of the topic: The cohomology space is governed by a vertex algebra that can be used to compute characteristic classes. contribution 0.54 0.46 0.14 asserted 1.00
s5 We present an implementation of the vertex operators in the rewriting logic system {\sc Maude} and address observations and conjectures obtained after symbolic computations. contribution 0.58 0.94 0.14 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.56 · evidence from proof or derivation 0.83.

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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 the study of the rational cohomology of Hilbert schemes of points on a smooth surface, it is particularly interesting to understand the characteristic classes of the tautological bundles and the tangent bundle. In this note we pursue this study. We first collect all results appearing separately in the literature and prove some new formulas using T. Ohmoto's results on orbifold Chern classes on Hilbert schemes. We also explain the algorithmic counterpart of the topic: The cohomology space is governed by a vertex algebra that can be used to compute characteristic classes. We present an implementation of the vertex operators in the rewriting logic system {\sc Maude} and address observations and conjectures obtained after symbolic computations.

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