Fano 3-folds of index 2

Details Fano 3-folds of index 2 Fano 3-folds of index 2

2006-11-28

arxiv.org/abs/math/0611862v1

Mathematics

Algebraic Geometry

19 pages

Scientific paper

We study Fano 3-folds with Fano index 2: that is, 3-folds X with rank Pic(X) = 1, Q-factorial terminal singularities and -K_X = 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 H^0(X,-K_X) and the sharp bound (-K_X)^3 >= 8/165. We list families that can be realised in codimension up to 4.

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