Kähler几何中的渐近Chow多稳定性
Asymptotic Chow polystability in Kähler geometry
摘要：
证明了常数数量曲率Kähler度量的存在性等价于K-稳定性，或K-多稳定性（取决于术语）（Yau-Tian-Donaldson猜想）.还有另一个GIT稳定性条件，称为渐近Chow多稳定性。这个条件意味着存在的平衡度量的极化流形$(M, L^k)$的所有大$k$。预期平衡度量收敛到恒定数量曲率度量，因为在进一步合适的稳定性条件下$k$趋于无穷大。在这篇调查文章中，我将报告最近的结果说，渐近周多稳定性不持有某些常数数量曲率凯勒流形。我们还比较了一份文件的小野与德拉维多瓦和祖达斯。
英文摘要：
It is conjectured that the existence of constant scalar curvature Kähler metrics will be equivalent to K-stability, or K-polystability depending on terminology (Yau-Tian-Donaldson conjecture). There is another GIT stability condition, called the asymptotic Chow polystability. This condition implies the existence of balanced metrics for polarized manifolds $(M, L^k)$ for all large $k$. It is expected that the balanced metrics converge to a constant scalar curvature metric as $k$ tends to infinity under further suitable stability conditions. In this survey article I will report on recent results saying that the asymptotic Chow polystability does not hold for certain constant scalar curvature Kähler manifolds. We also compare a paper of Ono with that of Della Vedova and Zuddas.
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