On Q-Fano threefolds of Fano index 2

Abstract

We show that, for a Q-Fano threefold X of Fano index 2, the inequality dim |-1/2K_X| <= 4 holds with a single well understood family of varieties having dim |-1/2K_X| = 4.

Minor changes, mostly biographical, to bring into line with the published version in Minimal Models and Extremal Rays (Kyoto 2011), Advanced Studies in Pure Mathematics 70, 2016, pp. 397--420

References in corpus (2)

• Fano 3-folds in codimension 4, Tom and Jerry, Part I
• On Fano indicies of Q-Fano 3-folds

Cited by in corpus (9)

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• Constructing Q-Fano 3-folds à la Prokhorov & Reid
• Toric G-solid Fano threefolds
• Rationality of Fano threefolds with terminal Gorenstein singularities, I
• Divisorial extractions from singular curves in a smooth 3-fold, II: low codimension
• Conic bundle structures on Q-Fano threefolds
• Rationality of $\mathbb{Q}$-Fano threefolds of large Fano index