Filtrations and test-configurations
By G'abor Sz'ekelyhidi. 2011
97 citations recorded by the source corpus.
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 $$b$$b-stability.
Subfields: Applied Mathematics, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a316db0da3d4e59b979f6031709e1ffa99830a94
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In Applied Mathematics
In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Uniform stability of twisted constant scalar curvature K\"ahler metrics (2014, background): “Indeed, it is expected that one needs to strengthen the definition of K-stability in the untwisted case in the statement of the Yau-Tian-Donaldson conjecture, by requiring uniformity with respect to some norm [47].”
- Optimal bounds for the volumes of Kähler-Einstein Fano manifolds (2015, result): “The construction is similar to the one in [Szé14].”
- Gromov–Hausdorff limits of Kähler manifolds and algebraic geometry, II (2015, background): “Notice as in [37], [33], a test configuration for W can also be viewed as a filtration on the coordinate ring of W .”