Filtrations and test-configurations
arXiv:1111.4986
Abstract
We introduce a strengthening of K-stability, based on filtrations of the homogeneous coordinate ring. This allows for considering certain limits of families of test-configurations, which arise naturally in several settings. We prove that if a manifold with no automorphisms admits a cscK metric, then it satisfies this stronger stability notion. We also discuss the relation with the birational transformations in the definition of b-stability.
34 pages, new appendix by S. Boucksom proving the conjecture in the earlier version
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- A remark on the Donaldson-Futaki invariant for sequences of test configurations