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The curve exclusion theorem for elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces

Part of: Birational geometry Surfaces and higher-dimensional varieties

Published online by Cambridge University Press:  02 February 2009

Daniel Ryder
Daniel Ryder
Affiliation:
Department of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, UK (daniel.ryder@bristol.ac.uk)
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Abstract

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The theorem referred to in the title is a technical result that is needed for the classification of elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces in weighted projective space. We present a complete proof of the curve exclusion theorem, which first appeared in the author's PhD thesis and has since been relied upon in solutions to many cases of the fibration classification problem. We give examples of these solutions and discuss them briefly.

Keywords

Fano3-foldelliptic fibrationK3 fibration

MSC classification

Secondary: 14J30: $3$-folds 14E05: Rational and birational maps
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 52 , Issue 1 , February 2009 , pp. 189 - 210
Copyright
Copyright © Edinburgh Mathematical Society 2009