论文标题
Fano歧管上的抗神经平衡指标
Anticanonically balanced metrics on Fano manifolds
论文作者
论文摘要
我们表明，如果Fano歧管具有离散的自动形态组，并接受了两极化的Kähler-Einstein指标，那么就存在一系列抗综合平衡的指标顺利地收敛到Kähler-Einstein Metric。我们的证明是基于简化了唐纳森（Donaldson）对平衡指标的类似结果的证明，通过使用berezin-toeplitz量化来代替微妙的几何论点。然后，我们将此结果应用于计算在反典型环境中唐纳森迭代的固定点的最佳收敛速率的渐近学。
We show that if a Fano manifold has discrete automorphism group and admits a polarized Kähler-Einstein metric, then there exists a sequence of anticanonically balanced metrics converging smoothly to the Kähler-Einstein metric. Our proof is based on a simplification of Donaldson's proof of the analogous result for balanced metrics, replacing a delicate geometric argument by the use of Berezin-Toeplitz quantization. We then apply this result to compute the asymptotics of the optimal rate of convergence to the fixed point of Donaldson's iterations in the anticanonical setting.
