On K-Polystability of cscK Manifolds with Transcendental Cohomology Class
Artikel i vetenskaplig tidskrift, 2020

In this paper we study K-polystability of arbitrary (possibly non-projective) compact Miller manifolds admitting holomorphic vector fields. As a main result we show that existence of a constant scalar curvature Kahler (cscK) metric implies geodesic K-polystability, in a sense that is expected to be equivalent to K-polystability in general. In particular, in the spirit of an expectation of Chen-Tang [28] we show that geodesic K-polystability implies algebraic K-polystability for polarized manifolds, so our main result recovers a possibly stronger version of results of Berman-Darvas-Lu [10] in this case. As a key part of the proof we also study subgeodesic rays with singularity type prescribed by singular test configurations and prove a result on asymptotics of the Kenergy functional along such rays. In an appendix by R. Dervan it is moreover deduced that geodesic K-polystability implies equivariant K-polystability. This improves upon the results of [39] and proves that existence of a cscK (or extremal) Miller metric implies equivariant K-polystability (resp. relative K-stability).

Författare

Zakarias Sjöström Dyrefelt

École polytechnique

Chalmers, Matematiska vetenskaper, Algebra och geometri

International Mathematics Research Notices

1073-7928 (ISSN) 1687-0247 (eISSN)

Vol. 2020 9 2769-2817

Ämneskategorier

Algebra och logik

Geometri

Matematisk analys

DOI

10.1093/imrn/rny094

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Senast uppdaterat

2020-11-09