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Title: A non-Archimedean approach to K-stability, II: Divisorial stability and openness
To any projective pair (X,B) equipped with an ample Q-line bundle L (or even any ample numerical class), we attach a new invariant $$\beta(\mu)$$, defined on convex combinations $$\mu$$ of divisorial valuations on X , viewed as point masses on the Berkovich analytification of X . The construction is based on non-Archimedean pluripotential theory, and extends the Dervan–Legendre invariant for a single valuation – itself specializing to Li and Fujita’s valuative invariant in the Fano case, which detects K-stability. Using our $$\beta$$-invariant, we define divisorial (semi)stability, and show that divisorial semistability implies (X,B) is sublc (i.e. its log discrepancy function is non-negative), and that divisorial stability is an open condition with respect to the polarization L. We also show that divisorial stability implies uniform K-stability in the usual sense of (ample) test configurations, and that it is equivalent to uniform K-stability with respect to all norms/filtrations on the section ring of (X,L), as considered by Chi Li.  more » « less
Award ID(s):
2154380 1900025 1600011
PAR ID:
10516582
Author(s) / Creator(s):
;
Publisher / Repository:
De Gruyter
Date Published:
Journal Name:
Journal für die reine und angewandte Mathematik (Crelles Journal)
Volume:
805
Issue:
0
ISSN:
0075-4102
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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