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

DJ Ryder

Research output: Contribution to journalArticle (Academic Journal)

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 contributionClassification of elliptic and K3 fibrations birational to some Q-Fano 3-folds
Original languageEnglish
Pages (from-to)13 - 42
Number of pages20
JournalJournal of Mathematical Sciences (University of Tokyo)
Volume13 (1)
Publication statusPublished - Jan 2006

Bibliographical note

Publisher: University of Tokyo

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