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arXiv · 2109.03453

Characterizing terminal Fano threefolds with the smallest anti-canonical volume

Chen Jiang
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Abstract

It was proved by J. A. Chen and M. Chen that a terminal Fano $3$-fold $X$ satisfies $(-K_X)^3\geq \frac{1}{330}$. We show that a non-rational $\mathbb{Q}$-factorial terminal Fano $3$-fold $X$ with $\rho(X)=1$ and $(-K_X)^3=\frac{1}{330}$ is a weighted hypersurface of degree $66$ in $\mathbb{P}(1,5,6,22,33)$.

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Chen Jiang. 2021-09-08. Characterizing terminal Fano threefolds with the smallest anti-canonical volume. https://doi.org/10.1007/978-3-031-17859-7_18

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