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The integral cohomology of the Hilbert scheme of points on a surface
Forum of Mathematics, Sigma ( IF 1.2 ) Pub Date : 2020-11-04 , DOI: 10.1017/fms.2020.35 Burt Totaro
Forum of Mathematics, Sigma ( IF 1.2 ) Pub Date : 2020-11-04 , DOI: 10.1017/fms.2020.35 Burt Totaro
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.
中文翻译:
曲面上点的希尔伯特方案的积分上同调
我们证明如果X 是具有无扭上同调的光滑复射影曲面,则 Hilbert 格式 $X^{[n]}$ 对每个自然数都有无扭上同调n . 这扩展了马克曼在泊松曲面情况下的早期工作。该证明使用 Gholampour-Thomas 的减少障碍理论用于嵌套的 Hilbert 曲面方案。
更新日期:2020-11-04
中文翻译:
曲面上点的希尔伯特方案的积分上同调
我们证明如果