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arXiv · 2304.11333

Birational rigidity and alpha invariants of Fano varieties

Ivan Cheltsov·Arman Sarikyan·Ziquan Zhuang
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Abstract

We prove that for every $ε>0$, there is a birationally super-rigid Fano variety $X$ such that $\frac{1}{2}\leqslantα(X)\leqslant \frac{1}{2}+ε$. Also we show that for every $ε>0$, there is a Fano variety $X$ and a finite subgroup $G\subset\mathrm{Aut}(X)$ such that $X$ is $G$-birationally super-rigid, and $α_G(X)<ε$.

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Ivan Cheltsov, Arman Sarikyan, Ziquan Zhuang. 2023-04-22. Birational rigidity and alpha invariants of Fano varieties. https://arxiv.org/abs/2304.11333

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