$\mathbb{Q}$-Fano threefolds with three birational Mori fiber structures

Abstract

In this paper we give first examples of $\mathbb{Q}$-Fano threefolds whose birational Mori fiber structures consist of exactly three $\mathbb{Q}$-Fano threefolds. These examples are constructed as weighted hypersurfaces in a specific weighted projective space. We also observe that the number of birational Mori fiber structures does not behave upper semi-continuously in a family of $\mathbb{Q}$-Fano threefolds.

24 pages, final version

References in corpus (5)

• Birationally rigid Fano threefold hypersurfaces
• Birational Mori fiber structures of Q-Fano 3-fold weighted complete intersections, II
• Birational rigidity is not an open property
• Birational Mori fiber structures of $\mathbb{Q}$-Fano $3$-fold weighted complete intersections, III
• Non-rigid quartic 3-folds

Cited by in corpus (1)

• Birational Mori fiber structures of $\mathbb{Q}$-Fano $3$-fold weighted complete intersections, III