Stability of anti-canonically balanced metrics
Stability of anti-canonically balanced metrics
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DOI：
10.4310/ajm.2019.v23.n6.a9
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发表时间：
2016-07
影响因子：
0.6
通讯作者：
Shunsuke Saito;Ryosuke Takahashi
中科院分区：
文献类型：
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作者：
Shunsuke Saito;Ryosuke Takahashi
我们研究了量子化 Ding 泛函沿 Bergman 测地射线的渐近行为，并证明无穷远处的斜率可以用 Donaldson-Futaki 不变量和 Chow 权重来表示。基于斜率公式，我们在 Fano 流形上引入了一种新的代数几何稳定性，并表明反正则平衡度量的存在意味着我们的稳定性。还讨论了我们的稳定性与其他稳定性之间的关系。作为斜率公式的另一个应用，我们得到了 Fano 流形上类 Calabi 泛函的下界估计。
We study the asymptotic behavior of quantized Ding functionals along Bergman geodesic rays and prove that the slope at infinity can be expressed in terms of Donaldson-Futaki invariants and Chow weights. Based on the slope formula, we introduce a new algebro-geometric stability on Fano manifolds and show that the existence of anti-canonically balanced metrics implies our stability. The relation between our stability and others is also discussed. As another application of the slope formula, we get the lower bound estimate on the Calabi like functionals on Fano manifolds.