Q-Fano threefolds of index $7$

Abstract

We show that, for a $\mathbb{Q}$-Fano threefold $X$ of Fano index 7, the inequality $\dim |-K_X|\ge 15$ implies that $X$ is isomorphic to one of the following varieties $\mathbb{P}(1^2,2,3)$, $X_6\subset \mathbb{P}(1,2^2,3,5)$ or $X_6\subset \mathbb{P}(1,2,3^2,4)$.

20 pages, LaTeX

Cited by in corpus (5)

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• Constructing Fano 3-folds from cluster varieties of rank 2
• On the birational geometry of $\mathbf{Q}$-Fano threefolds of large Fano index, I
• Standard models of degree $1$ del Pezzo fibrations
• Log canonical degenerations of del Pezzo surfaces in Q-Gorenstein families