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The integral cohomology of the Hilbert scheme of points on a surface

Part of: Fiber spaces and bundles Cycles and subschemes

Published online by Cambridge University Press:  04 November 2020

Burt Totaro Open the ORCID record for Burt Totaro [Opens in a new window]
Burt Totaro*
Affiliation:
UCLA Mathematics Department, Box 951555, Los Angeles, CA90095-1555,USA; E-mail: totaro@math.ucla.edu

Abstract

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We show that if X is a smooth complex projective surface with torsion-free cohomology, then the Hilbert scheme $X^{[n]}$ has torsion-free cohomology for every natural number n. This extends earlier work by Markman on the case of Poisson surfaces. The proof uses Gholampour-Thomas’s reduced obstruction theory for nested Hilbert schemes of surfaces.

Keywords

Hilbert scheme of pointsintegral cohomologyChow motive

MSC classification

Primary: 14C05: Parametrization (Chow and Hilbert schemes)
Secondary: 55R80: Discriminantal varieties, configuration spaces
Type
Algebraic and Complex Geometry
Information
Forum of Mathematics, Sigma , Volume 8 , 2020 , e40
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2020. Published by Cambridge University Press

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