代数环面作用的Kempf-Ness集的拓扑
Topology of Kempf-Ness sets for algebraic torus actions
摘要：
在仿射簇上的代数群作用理论中，Kempf-Ness集的概念被用来用关于极大紧子群的商来代替范畴商。通过利用最近的成就“环面拓扑”，我们表明，一个适当的概念Kempf-Ness集存在一类代数环面行动拟仿射簇（坐标子空间安排补充）所产生的Batyrev-Cox“几何不变理论”的方法，环面品种。我们继续研究这些“环面”Kempf-Ness集的上同调。在射影非奇异环面簇的情况下，Kempf-Ness集可以描述为复空间中实二次曲面的完全交。
英文摘要：
In the theory of algebraic group actions on affine varieties, the concept of a Kempf-Ness set is used to replace the categorical quotient by the quotient with respect to a maximal compact subgroup. By making use of the recent achievements of "toric topology" we show that an appropriate notion of a Kempf-Ness set exists for a class of algebraic torus actions on quasiaffine varieties (coordinate subspace arrangement complements) arising in the Batyrev-Cox "geometric invariant theory" approach to toric varieties. We proceed by studying the cohomology of these "toric" Kempf-Ness sets. In the case of projective non-singular toric varieties the Kempf-Ness sets can be described as complete intersections of real quadrics in a complex space.
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