Fano 3-folds of index 2
Abstract
We study Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X) = 1, Q-factorial terminal singularities and -KX = 2A for an ample Weil divisor A. We give a first classification of all possible Hilbert series of such polarised varieties X,A and deduce both the nonvanishing of H0(X,-KX) and the sharp bound (-KX)3 >= 8/165. We list families that can be realised in codimension up to 4.
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