Pluripotential-Theoretic Stability Thresholds

Journal article, 2023

Given a compact polarized manifold (X , L), we introduce two new stability thresholds in terms of singularity types of global quasi-plurisubharmonic functions on X. We prove that in the Fano setting, the new invariants can effectively detect K-stability of X. We study some functionals of geodesic rays in the space of Miller potentials by means of the corresponding test curves. In particular, we introduce a new entropy functional of quasi-plurisubharmonic functions and relate the radial entropy functional to this new entropy functional.