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Generating Series in the Cohomology of Hilbert Schemes of Points on Surfaces

Published online by Cambridge University Press:  01 February 2010

Samuel Boissière  and
Marc A. Nieper-Wisskirchen
Samuel Boissière
Affiliation:
Laboratoire J. A. Dieudonné, UMR CNRS 6621, Université de Nice Sophia-AntipolisParc Valrose, 06108 Nice, France, sb@math.unice.fr, http://math.unice.fr/~sb
Marc A. Nieper-Wisskirchen
Affiliation:
Institut für Mathematik,, Johannes-Gutenberg Universität, 55099 Mainz, Germany, nieper@mathematik.uni-mainz, http://www.mathematik.uni-mainz.de/Members/nieper

Abstract

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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 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 MAUDE, and address observations and conjectures obtained after symbolic computations.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 10 , 2007 , pp. 254 - 270
Copyright
Copyright © London Mathematical Society 2007

References

reference

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Supplementary material: File

JCM 10 Boissiere and Nieper-Wisskirchen Appendix A

Boissiere and Nieper-Wisskirchen Appendix A

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