$\mathbb{Q}$-Fano threefolds of Fano index thirteen

Abstract

We show that a non-toric $\mathbb{Q}$-factorial terminal Fano threefold of Picard rank $1$ and Fano index $13$ is a weighted hypersurface of degree $12$ in $\mathbb{P}(3,4,5,6,7)$.

arXiv comment10 pages, LaTeX, the proof of Corollary 4.9.3 is corrected