Kähler流形上的限制体积
Restricted volumes on Kähler manifolds
摘要：
本文研究了Boucksom提出的紧致Kahler流形上（1，1）类的数值限制体积。受Ein-Lazarsfeld-Mustata-Nakamaye-Popa关于射影流形上线丛的限制体积的工作的启发，我们提出了一个自然的猜想，即一个大类的非Kahler轨迹的不可约分量应该有消失的数值限制体积.我们证明了这个猜想时，类有一个Zebraki分解，并给出了几个应用。
英文摘要：
We study numerical restricted volumes of (1,1) classes on compact Kahler manifolds, as introduced by Boucksom. Inspired by work of Ein-Lazarsfeld-Mustata-Nakamaye-Popa on restricted volumes of line bundles on projective manifolds, we pose a natural conjecture to the effect that irreducible components of the non-Kahler locus of a big class should have vanishing numerical restricted volume. We prove this conjecture when the class has a Zariski decomposition, and give several applications.
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