English

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

Algebraic Geometry 2026-01-22 v3

Abstract

We show that a non-toric Q\mathbb{Q}-factorial terminal Fano threefold of Picard rank 11 and Fano index 1313 is a weighted hypersurface of degree 1212 in P(3,4,5,6,7)\mathbb{P}(3,4,5,6,7).

Keywords

Cite

@article{arxiv.2212.06884,
  title  = {$\mathbb{Q}$-Fano threefolds of Fano index thirteen},
  author = {Yuri Prokhorov},
  journal= {arXiv preprint arXiv:2212.06884},
  year   = {2026}
}

Comments

10 pages, LaTeX, the proof of Corollary 4.9.3 is corrected