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The Curve Exclusion Theorem for elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces

Daniel Ryder
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Abstract

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 We present a complete proof of the Curve Exclusion Theorem, which first appeared in the author's unpublished PhD thesis [Ry02] and has since been relied upon in solutions to many cases of the fibration classification problem.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.

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Daniel Ryder. 2006-06-08. The Curve Exclusion Theorem for elliptic and K3 fibrations birational to Fano 3-fold hypersurfaces. https://arxiv.org/abs/math/0606177

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