用Kähler-里奇流II收缩例外因子
Contracting exceptional divisors by the Kähler-Ricci flow II
摘要：
研究了Kahler-里奇流将具有O（-k）正规丛的不相交例外因子吹到轨道点的情形.证明了例外因子外的光滑收敛性和全局格罗莫夫-豪斯多夫收敛。另外，我们还建立了在流下Gromov-Hausdorff极限与极限度量的度量完备一致的结果。这改进和扩展了作者以前的工作。我们将其应用于P^1-丛，它是Hirzebruch曲面的高维类似物。此外，我们考虑了一般类型的极小曲面的情形，证明了归一化Kahler-里奇流的解在Gromov-Hausdorff意义下收敛于Kahler-Einstein轨道。
英文摘要：
We investigate the case of the Kahler-Ricci flow blowing down disjoint exceptional divisors with normal bundle O(-k) to orbifold points. We prove smooth convergence outside the exceptional divisors and global Gromov-Hausdorff convergence. In addition, we establish the result that the Gromov-Hausdorff limit coincides with the metric completion of the limiting metric under the flow. This improves and extends the previous work of the authors. We apply this to P^1-bundles which are higher-dimensional analogues of the Hirzebruch surfaces. In addition, we consider the case of a minimal surface of general type with only distinct irreducible (-2)-curves and show that solutions to the normalized Kahler-Ricci flow converge in the Gromov-Hausdorff sense to a Kahler-Einstein orbifold.
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