On non-rigid del Pezzo fibrations of low degree

Abstract

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.

34 pages

References in corpus (1)

• Birational Geometry of 3-fold Mori Fibre Spaces

Cited by in corpus (4)

• Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, II
• Non-rigid quartic 3-folds
• On pliability of del Pezzo fibrations and Cox rings
• On birational rigidity of singular del Pezzo fibrations of degree 1