摘要翻译:
研究仿射Grassmannian上的拓扑群结构(由环乘法得到)。特别地,我们研究了生成同调环的有限维子簇。我们证明存在一个生成舒伯特变体的规范族,即那些由与最高根相关的coroot的负定义的变体。这些不仅产生了同调,而且产生了精确意义上的仿射Grassmannian本身。
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英文标题:
《Generating varieties for affine Grassmannians》
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作者:
Peter J. Littig and Stephen A. Mitchell
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最新提交年份:
2008
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分类信息:
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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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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英文摘要:
We study the topological group structure (coming from loop multiplication) on an affine Grassmannian. In particular, we study finite-dimensional subvarieties that generate the homology ring. We show that there is a canonical family of generating Schubert varieties, namely those defined by the negative of the coroot associated to the highest root. These not only generate the homology, but generate the affine Grassmannian itself in a precise sense.
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PDF链接:
https://arxiv.org/pdf/0810.3266