Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics
International Mathematics Research Notices
Oxford University Press
MetadataShow full item record
Dervan, R. (2015). Uniform Stability of Twisted Constant Scalar Curvature Kähler Metrics. International Mathematics Research Notices https://doi.org/10.1093/imrn/rnv291
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.
The author was funded by a studentship associated to an EPSRC Career Acceleration Fellowship (EP/J002062/1).
External DOI: https://doi.org/10.1093/imrn/rnv291
This record's URL: https://www.repository.cam.ac.uk/handle/1810/255085