用Kähler-里奇流收缩例外因子
Contracting exceptional divisors by the Kähler-Ricci flow
摘要：
本文给出了Kahler-里奇流的解g（t）在紧致流形上收缩例外因子并在新流形上唯一连续的一个判据.当t从每个方向趋于奇异时间T时，我们证明了g（t）在Gromov-Hausdorff意义下的收敛性和远离例外因子的光滑收敛性.我们称这种行为的Kahler-里奇流的一个典型的外科收缩。特别地，我们的结果表明射影代数曲面上的Kahler-里奇流将进行一系列规范的外科手术收缩，直到在有限时间内，要么得到极小模型，要么流形的体积趋于零.
英文摘要：
We give a criterion under which a solution g(t) of the Kahler-Ricci flow contracts exceptional divisors on a compact manifold and can be uniquely continued on a new manifold. As t tends to the singular time T from each direction, we prove convergence of g(t) in the sense of Gromov-Hausdorff and smooth convergence away from the exceptional divisors. We call this behavior for the Kahler-Ricci flow a canonical surgical contraction. In particular, our results show that the Kahler-Ricci flow on a projective algebraic surface will perform a sequence of canonical surgical contractions until, in finite time, either the minimal model is obtained, or the volume of the manifold tends to zero.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
