klt对上的Demailly-Kollár连续性及其在alpha和delta不变量中的应用
Demailly-Kollár continuity on klt pairs, and applications to alpha and delta invariants
AI总结：
该研究建立了klt对上的Demailly-Kollár型连续性定理，证明了两类alpha与delta不变量的版本相等，解决了相关猜想并给出了扭曲Kähler-Einstein方程可解性的新判据。
AI中文摘要：
我们针对正规复解析klt对，建立了关于适配测度的多重次调和函数的Demailly-Kollár型连续性定理。作为应用，我们证明了紧正规Kähler klt对上alpha和delta不变量的解析版本与除子版本相等，从而完成了第二作者发起的研究计划。我们进一步证明了Guedj与Trusiani引入的孤立对数终端奇点的两个局部alpha不变量重合，且其公共值为Li的正规化体积的n次方根。这些恒等式具有几何推论：delta不变量的等式给出了大上同调类中扭曲Kähler-Einstein方程可解性的Yau-Tian-Donaldson型除子判据，无需对扭曲项作半正性假设；局部alpha恒等式代数地确定了控制孤立对数终端奇点附近正曲率KE度量存在性的临界指数，从而证实了Guedj与Trusiani的猜想。
英文摘要：
We establish a Demailly-Kollár type continuity theorem for plurisubharmonic functions with respect to adapted measures on normal complex analytic klt pairs. As applications, we prove the equality of the analytic and divisorial versions of the alpha and delta invariants on compact normal Kähler klt pairs, thereby completing a program initiated by the second author. We further show that the two local alpha invariants introduced by Guedj and Trusiani for an isolated log terminal singularity coincide and that their common value is the $n$th root of Li's normalized volume. These identities have geometric consequences. The equality for the delta invariant yields a Yau-Tian-Donaldson type divisorial criterion for the solvability of twisted Kähler-Einstein equations in big cohomology classes, without a semipositivity assumption on the twist. The local alpha identity determines algebraically the critical exponent governing the existence of positively curved KE metrics near an isolated log terminal singularity, thus confirming a prediction of Guedj and Trusiani.
