## Abstract

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 $\PP^4$ 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 $\XnH$, where $\HH$ is the linear system associated to the putative birational map and $n$ is its anticanonical degree.

Translated title of the contribution | Classification of elliptic and K3 fibrations birational to some Q-Fano 3-folds |
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Original language | English |

Pages (from-to) | 13 - 42 |

Number of pages | 20 |

Journal | Journal of Mathematical Sciences (University of Tokyo) |

Volume | 13 (1) |

Publication status | Published - Jan 2006 |