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.
雑誌名
Journal of mathematical sciences, the University of Tokyo
巻
13
号
1
ページ
13 - 42
発行年
2006-03-21
ISSN
13405705
書誌レコードID
AA11021653
フォーマット
application/pdf
日本十進分類法
415
Mathmatical Subject Classification
14E05(MSC1991)
14J30(MSC1991)
14E30(MSC1991)
出版者
Graduate School of Mathematical Sciences, The University of Tokyo
原稿受領日
2005-10-14
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Classfication of elliptic and K3 fibrations birational to some Q-Fano 3 folds
jms130102.pdf
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