Classification of elliptic and K3 fibrations birational to some Q-Fano 3-folds

Details Classification of elliptic and K3 fibrations birational to some Q-Fano 3-folds Classification of elliptic and K3 fibrations birational to some Q-Fano 3-folds

2005-08-24

arxiv.org/abs/math/0508467v1

Mathematics

Algebraic Geometry

24 pages

Scientific paper

A complete classification is presented of elliptic and K3 fibrations birational to certain mildly singular complex Fano 3-folds. Detailed proofs are given for one example case, namely that of a general hypersurface X of degree 30 in weighted P^4 with weights 1,4,5,6,15; but our methods apply more generally. For constructing birational maps from X to elliptic and K3 fibrations we use Kawamata blowups and Mori theory to compute anticanonical rings; to exclude other possible fibrations we make a close examination of the strictly canonical singularities of (X,(1/n)H), where H is the linear system associated to the putative birational map and n is its anticanonical degree.

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