摘要翻译:
证明了一个表示非紧简连通曲面上点的Hilbert格式的切丛上的任意乘性特征类的闭式。作为推论,我们导出了这些Hilbert格式切丛Chern特征的一个封闭公式。我们还给出了曲面上线丛所对应的重言丛的乘法特征类的一个闭式。最后,我们讨论了本文结果对任意曲面点的Hilbert格式的含义。
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英文标题:
《Characteristic classes of the Hilbert schemes of points on non-compact
simply-connected surfaces》
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作者:
Marc Nieper-Wisskirchen
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Algebraic Geometry 代数几何
分类描述:Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇,叠,束,格式,模空间,复几何,量子上同调
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一级分类:Mathematics 数学
二级分类:Algebraic Topology 代数拓扑
分类描述:Homotopy theory, homological algebra, algebraic treatments of manifolds
同伦理论,同调代数,流形的代数处理
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英文摘要:
We prove a closed formula expressing any multiplicative characteristic class evaluated on the tangent bundle of the Hilbert schemes of points on a non-compact simply-connected surface. As a corollary, we deduce a closed formula for the Chern character of the tangent bundles of these Hilbert schemes. We also give a closed formula for the multiplicative characteristic classes of the tautological bundles associated to a line bundle on the surface. We finally remark which implications the results here have for the Hilbert schemes of points of an arbitrary surface.
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PDF链接:
https://arxiv.org/pdf/0707.3268