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

arXiv eprints
 Pub Date:
 December 2020
 DOI:
 10.48550/arXiv.2012.12039
 arXiv:
 arXiv:2012.12039
 Bibcode:
 2020arXiv201212039X
 Keywords:

 Mathematics  Differential Geometry;
 Mathematics  Algebraic Geometry;
 Mathematics  Complex Variables
 EPrint:
 Final version, to appear on IMRN