Filtrations and test-configurations
Algebraic Geometry
2013-02-15 v2 Differential Geometry
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.
Cite
@article{arxiv.1111.4986,
title = {Filtrations and test-configurations},
author = {Gábor Székelyhidi},
journal= {arXiv preprint arXiv:1111.4986},
year = {2013}
}
Comments
34 pages, new appendix by S. Boucksom proving the conjecture in the earlier version