Pluripotential-theoretic stability thresholds
Abstract
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 the K-stability 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 quasi-plurisubharmonic functions and relate the radial entropy functional to this new entropy functional.
- Publication:
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arXiv e-prints
- Pub Date:
- December 2020
- DOI:
- 10.48550/arXiv.2012.12039
- arXiv:
- arXiv:2012.12039
- Bibcode:
- 2020arXiv201212039X
- Keywords:
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- Mathematics - Differential Geometry;
- Mathematics - Algebraic Geometry;
- Mathematics - Complex Variables
- E-Print:
- Final version, to appear on IMRN