Geodesic
The integral cohomology of the Hilbert scheme of points on a surface
Forum of Mathematics, Sigma, Tome 8 (2020)

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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. 
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     author = {Burt Totaro},
     title = {The integral cohomology of the {Hilbert} scheme of points on a surface},
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     year = {2020},
     doi = {10.1017/fms.2020.35},
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     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2020.35/}
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Burt Totaro. The integral cohomology of the Hilbert scheme of points on a surface. Forum of Mathematics, Sigma, Tome 8 (2020). doi: 10.1017/fms.2020.35

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