Characterizing terminal Fano threefolds with the smallest anti-canonical volume

Abstract

It was proved by J. A. Chen and M. Chen that a terminal Fano $3$-fold $X$ satisfies $(-K_X{)}^3\ge \frac{1}{330}$. 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 $\mathbb{P}(1,5,6,22,33)$.

6 pages

Cited by in corpus (2)

• On the anti-canonical geometry of weak $\mathbb{Q}$-Fano threefolds, III
• The Noether inequality for threefolds and three moduli spaces with minimal volumes