Uniform Stability of Twisted Constant Scalar Curvature Kahler Metrics

作者：Dervan Ruadhai^*

来源：International Mathematics Research Notices, 2016, 2016(15): 4728-4783.

DOI：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 Kahler 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 L-2-norm, if and only if it is almost trivial.
We prove the existence of a twisted constant scalar curvature Kahler 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.

• 出版日期2016