K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

In-Kyun Kim; Takuzo Okada; Joonyeong Won

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

Algebraic Geometry 2023-08-29 v3

Authors: In-Kyun Kim , Takuzo Okada , Joonyeong Won

Abstract

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 \cite{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 $1$ .

Keywords

k-stability fano 3-fold weighted hypersurface birational superrigidity alpha invariant quasi-smooth

Cite

@article{arxiv.2011.07512,
  title  = {K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces},
  author = {In-Kyun Kim and Takuzo Okada and Joonyeong Won},
  journal= {arXiv preprint arXiv:2011.07512},
  year   = {2023}
}

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119 pages. Final version

K-stability of birationally superrigid Fano 3-fold weighted hypersurfaces

Abstract

Keywords

Cite

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