K-STABILITY OF FANO MANIFOLDS WITH NOT SMALL ALPHA INVARIANTS

By Kento Fujita. Journal of the Institute of Mathematics of Jussieu, 2016

56 citations recorded by the source corpus.

We show that any $n$ -dimensional Fano manifold $X$ with $\unicode[STIX]{x1D6FC}(X)=n/(n+1)$ and $n\geqslant 2$ is K-stable, where $\unicode[STIX]{x1D6FC}(X)$ is the alpha invariant of $X$ introduced by Tian. In particular, any such $X$ admits Kähler–Einstein metrics and the holomorphic automorphism group $\operatorname{Aut}(X)$ of $X$ is finite.

Subfields: Applied Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/0cfa827b79795ce0ae4ae78b1896106d09b17503

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In Applied Mathematics

1. Mattias Jonsson
2. H. Blum
3. Chi Li
4. Cristiano Spotti
5. Song Sun
6. Yuchen Liu
7. Chenyang Xu
8. Robert J. Berman

In Geometry and Topology

1. H. Blum
2. Chi Li
3. Mattias Jonsson
4. Cristiano Spotti
5. Chenyang Xu
6. Yuchen Liu
7. Song Sun
8. S. Boucksom

Citations in the corpus

• Thresholds, valuations, and K-stability (2017, background): “> n n+1 ), then Xis K-semistable (resp. uniformly K-stable), thus recovering results in [OSa12, BHJ17, Der16, FO18], that can be viewed as algebraic versions of Tian’s theorem in [Tia97]. See also [Fuj19b] for the case ( K X) = n n+1 , and [Der15] for more general polarizations. 1The idea of the ”
• Explicit Gromov-Hausdorff compactifications of moduli spaces of K\"ahler-Einstein Fano manifolds (2017, background): “se of degree four del Pezzos to conclude. Another example (with much smaller anticanonical volume) we like to briefly discuss is the case of quartic hypersurfaces in CP4. By very recent work of Fujita [26], it is known that all smooth quartics admit KE metrics. However, by classification of smooth Fan”