Filtrations and test-configurations
G\'abor Sz\'ekelyhidi

TL;DR
This paper introduces a strengthened form of K-stability using filtrations, enabling the analysis of limits of test-configurations and linking stability to the existence of cscK metrics.
Contribution
It proposes a new stability notion based on filtrations, extending the framework of K-stability and connecting it to birational transformations and b-stability.
Findings
Manifolds with no automorphisms and cscK metrics satisfy the new stability.
The new stability notion considers limits of test-configurations.
Discussion of relations between this stability and b-stability.
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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Geometric Analysis and Curvature Flows · Advanced Algebra and Geometry
