的等变K-理论中的正性与Kleiman横截性 齐次空间

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摘要翻译：
本文证明了Graham-Kumar和Griffeth-Ram关于广义旗形群G/P的环面等变K理论结构常数中符号交替的猜想。这些结果是齐次空间及其子类的Borel混合空间在有限轨道的自然群作用下的等变同调Kleiman横截性原理的直接结果。利用S.Sierra引起的不可传递群作用的同调横截定理，将子群的等变K-类的舒伯特类展开中系数的计算归结为欧拉特征。当子簇有有理奇点时，一个消失定理表明欧拉特征最多是一个项--顶项--与一个定义良好的符号的和。通过适当地修正普通K-理论中由M.Brion引起的使Kawamata-Viehweg消失成立的几何论点，证明了该消失。
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英文标题：
《Positivity and Kleiman transversality in equivariant K-theory of
  homogeneous spaces》
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作者：
Dave Anderson, Stephen Griffeth, and Ezra Miller
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最新提交年份：
2017
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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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英文摘要：
  We prove the conjectures of Graham-Kumar and Griffeth-Ram concerning the alternation of signs in the structure constants for torus-equivariant K-theory of generalized flag varieties G/P. These results are immediate consequences of an equivariant homological Kleiman transversality principle for the Borel mixing spaces of homogeneous spaces, and their subvarieties, under a natural group action with finitely many orbits. The computation of the coefficients in the expansion of the equivariant K-class of a subvariety in terms of Schubert classes is reduced to an Euler characteristic using the homological transversality theorem for non-transitive group actions due to S. Sierra. A vanishing theorem, when the subvariety has rational singularities, shows that the Euler characteristic is a sum of at most one term--the top one--with a well-defined sign. The vanishing is proved by suitably modifying a geometric argument due to M. Brion in ordinary K-theory that brings Kawamata-Viehweg vanishing to bear.
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PDF链接：
https://arxiv.org/pdf/0808.2785

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关键词：Kleim LEI ima Man coefficients characteristic 当子 广义 归结为 定理