On non-rigid del Pezzo fibrations of low degree

Details On non-rigid del Pezzo fibrations of low degree On non-rigid del Pezzo fibrations of low degree

2010-10-22

arxiv.org/abs/1010.4774v3

Mathematics

Algebraic Geometry

34 pages

Scientific paper

We consider $\mathbb{P}(1,1,1,2)$ bundles over $\mathbb{P}^1$ and construct hypersurfaces of these bundles which form a degree 2 del Pezzo fibration over $\mathbb{P}^1$ as a Mori fibre space. We classify all such hypersurfaces whose type $\III$ or $\IV$ Sarkisov links pass to a different Mori fibre space. A similar result for cubic surface fibrations over $\mathbb{P}^2$ is also presented.

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