Uniform stability of twisted constant scalar curvature Kähler metrics

Dervan, R. (2016) Uniform stability of twisted constant scalar curvature Kähler metrics. International Mathematics Research Notices, 2016(15), pp. 4728-4783. (doi: 10.1093/imrn/rnv291)

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We introduce a norm on the space of test configurations, called the minimum norm. We conjecture that uniform K-stability is equivalent to the existence of a constant scalar curvature Kähler metric. This uniformity is analogous to coercivity of the Mabuchi functional. We show that a test configuration has zero minimum norm if and only if it has zero L2-norm, if and only if it is almost trivial. We prove the existence of a twisted constant scalar curvature Kähler metric that implies uniform twisted K-stability with respect to the minimum norm. We give algebro-geometric proofs of uniform K-stability in the general type and Calabi-Yau cases, as well as Fano case under an alpha invariant condition. Our results hold for nearby line bundles, and in the twisted setting.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Dervan, Dr Ruadhaí
Authors: Dervan, R.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:International Mathematics Research Notices
Publisher:Oxford University Press
ISSN (Online):1687-0247
Published Online:14 October 2015

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