Uniform K-stability and plt blowups of log Fano pairs

By Kento Fujita. Kyoto Journal of Mathematics, 2017

69 citations recorded by the source corpus.

We show relationships between uniform K-stability and plt blowups of log Fano pairs. We see that it is enough to evaluate certain invariants defined by volume functions for all plt blowups in order to test uniform K-stability of log Fano pairs. We also discuss the uniform K-stability of two log Fano pairs under crepant finite covers. Moreover, we give another proof of K-semistability of the projective plane.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/963c4b35a6c87613f375f2cc98984c7b032411fd

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In Applied Mathematics

1. Chi Li
2. Mattias Jonsson
3. H. Blum
4. S. Boucksom
5. Robert J. Berman
6. G. Tian
7. Yuchen Liu
8. Feng Wang

In Geometry and Topology

1. Chi Li
2. Mattias Jonsson
3. H. Blum
4. S. Boucksom
5. Robert J. Berman
6. G. Tian
7. Yuchen Liu
8. Feng Wang

Citations in the corpus

• A non-Archimedean approach to K-stability (2018, background): “For the convenience of the reader, we compare our notation with the one in Fujita [Fuj16, Fuj17] .”
• Thresholds, valuations, and K-stability (2017, result): “(L) and (L) in Theorem A follow from estimates 1 n+1 T(v) S(v) T(v) that are proved along the way. When Lis ample and vis divisorial, the stronger inequality S(v) n n+1 T(v) was proved by Fujita [Fuj19c]. We deduce from results in [BKMS16] that the invariants S(v) and T(v) only depend on the numeri”
• Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds (2017, result): “s of Ka¨hler-Einstein Fano manifolds. By the result in [13] this amounts to verify the K-stability for a given Fano manifold. There have been important recent progresses towards this, see for example [28, 26, 27, 51] as well as older results based on α-invariant/log canonical threshold and multiplie”
• On the Yau‐Tian‐Donaldson Conjecture for Singular Fano Varieties (2017, methodology): “This is achieved by using the valuative criterions for K-stability developed in [25, 27, 38, 42].”