Uniform K-stability and asymptotics of energy functionals in Kähler geometry
Artikel i vetenskaplig tidskrift, 2019

Consider a polarized complex manifold (X, L) and a ray of positive metrics on L defined by a positive metric on a test configuration for (X, L). For many common functionals in Kähler geometry, we prove that the slope at infinity along the ray is given by evaluating the non-Archimedean version of the functional (as defined in our earlier paper [BHJ17]) at the non-Archimedean metric on L defined by the test configuration. Using this asymptotic result, we show that coercivity of the Mabuchi functional implies uniform K-stability, as defined in [Der15, BHJ17]. As a partial converse, we show that uniform K-stability implies coercivity of the Mabuchi functional when restricted to Bergman metrics.

Kähler geometry

K-stability

Non-Archimedean geometry

Canonical metrics

Författare

Sebastien Boucksom

Centre de Mathematiques Laurent Schwartz Ecole polytechnique

Tomoyuki Hisamoto

Nagoya University

Mattias Jonsson

Matematik

University of Michigan

Journal of the European Mathematical Society

1435-9855 (ISSN) 1435-9863 (eISSN)

Vol. 21 9 2905-2944

Ämneskategorier

Geometri

Diskret matematik

Matematisk analys

DOI

10.4171/JEMS/894

Mer information

Senast uppdaterat

2019-11-10