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.

中文翻译：

---

反规范平衡指标的稳定性

我们研究了量化的Ding泛函沿着Bergman测地线的渐近行为，并证明了无穷大的斜率可以用Donaldson–Futaki不变量和Chow权重表示。基于斜率公式，我们在Fano流形上引入了新的代数几何稳定性，并证明了反规范平衡度量的存在暗示了我们的稳定性。我们还讨论了我们的稳定与他人之间的关系。作为斜率公式的另一个应用，我们获得了Fano流形上类似Calabi的泛函的下界估计。