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