摘要翻译:
我们计算了局部常数方程组中有值曲面上点的Hilbert格式的上同调空间。为此,我们将I.Grojnoswki和H.Nakajima关于普通上同调的Fock空间描述推广到扭曲情形。我们将M.Lehn关于Virasoro代数作用的工作进一步推广到扭曲情形。以M.Lehn和Ch的工作为基础。然后,当曲面有一个数值上平凡的正则因子时,我们给出了扭曲情形下杯积的显式描述。我们以同样适用于射影和非射影情形的方式来表述我们的结果。作为我们方法的应用,我们给出了推广的Kummer类的上同调环和一系列偶维Calabi-Yau流形的上同调环的显式模型。
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英文标题:
《Twisted cohomology of the Hilbert schemes of points on surfaces》
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作者:
Marc A. 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 calculate the cohomology spaces of the Hilbert schemes of points on surfaces with values in locally constant systems. For that purpose, we generalise I. Grojnoswki's and H. Nakajima's description of the ordinary cohomology in terms of a Fock space representation to the twisted case. We further generalise M. Lehn's work on the action of the Virasoro algebra to the twisted case. Building on work by M. Lehn and Ch. Sorger, we then give an explicit description of the cup-product in the twisted case whenever the surface has a numerically trivial canonical divisor. We formulate our results in a way that they apply to the projective and non-projective case in equal measure. As an application of our methods, we give explicit models for the cohomology rings of the generalised Kummer varieties and of a series of certain even dimensional Calabi--Yau manifolds.
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PDF链接:
https://arxiv.org/pdf/0708.1437