期权、估值和K稳定性
Thresholds, valuations, and K-stability
摘要：
设X是正规复射影簇，L是X上的大线丛，最坏有klt个奇点.我们使用赋值来研究L的对数典型阈值，以及另一个不变量，稳定性阈值。后者推广了Fujita和Odaka的一个概念，并且可以用来刻画Q-Fano簇何时是K-半稳定的或一致K-稳定的。它也可以用来推广Fujita和Liu的体积界。这两个阈值可以写成X上赋值空间上某些泛函的下确界。当L是充分的，我们证明了这些infima达到。在复曲面情形下，复曲面赋值得到了这些下确界，并且我们得到了关于L的矩多面体的两个阈值的简单表达式。
英文摘要：
Let X be a normal complex projective variety with at worst klt singularities, and L a big line bundle on X. We use valuations to study the log canonical threshold of L, as well as another invariant, the stability threshold. The latter generalizes a notion by Fujita and Odaka, and can be used to characterize when a Q-Fano variety is K-semistable or uniformly K-stable. It can also be used to generalize volume bounds due to Fujita and Liu. The two thresholds can be written as infima of certain functionals on the space of valuations on X. When L is ample, we prove that these infima are attained. In the toric case, toric valuations acheive these infima, and we obtain simple expressions for the two thresholds in terms of the moment polytope of L.
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。
