Demailly-Kollár continuity on klt pairs, and applications to alpha and delta invariants
Abstract
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 nth 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.
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BibTeX
@misc{darvas2026demaillykollár,
title = {{Demailly-Kollár continuity on klt pairs, and applications to alpha and delta invariants}},
author = {Tamás Darvas and Kewei Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.23505},
eprint = {2608.23505},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.23505},
}
RIS
TY - UNPB
TI - Demailly-Kollár continuity on klt pairs, and applications to alpha and delta invariants
AU - Tamás Darvas
AU - Kewei Zhang
PY - 2026
DA - 2026/09/13
PB - arXiv
DO - 10.48550/arxiv.2608.23505
UR - https://arxiv.org/abs/2608.23505
AB - 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 nth 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.
ER -