Geodesic
K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces
Forum of Mathematics, Sigma, Tome 11 (2023)

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We prove that the alpha invariant of a quasi-smooth Fano 3-fold weighted hypersurface of index $1$ is greater than or equal to $1/2$. Combining this with the result of Stibitz and Zhuang [SZ19] on a relation between birational superrigidity and K-stability, we prove the K-stability of a birationally superrigid quasi-smooth Fano 3-fold weighted hypersurfaces of index $1$. 
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     author = {In-Kyun Kim and Takuzo Okada and Joonyeong Won},
     title = {K-stability of birationally superrigid {Fano} 3-fold weighted hypersurfaces},
     journal = {Forum of Mathematics, Sigma},
     publisher = {mathdoc},
     volume = {11},
     year = {2023},
     doi = {10.1017/fms.2023.87},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/fms.2023.87/}
}
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In-Kyun Kim; Takuzo Okada; Joonyeong Won. K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces. Forum of Mathematics, Sigma, Tome 11 (2023). doi: 10.1017/fms.2023.87

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