Birationally rigid iterated Fano double covers

Abstract

Iterating the procedure of making a double cover over a given variety, we construct large families of smooth higher-dimensional Fano varieties of index 1. These varieties can be realized as complete intersections in various weighted projective spaces. A generic variety in these families is proved to be birationally superrigid; in particular, it admits no non-trivial structures of a fibration into rationally connected (or uniruled) varieties, it is non-rational and its groups of birational and biregular self-maps coincide.

51 pages

References in corpus (4)

• Birationally rigid Fano hypersurfaces
• Essentials of the method of maximal singularities
• Birational rigidity of a three-dimensional double cone
• Birational properties of pencils of del Pezzo surfaces of degree 1 and 2

Cited by in corpus (11)

• Birationally rigid varieties with a pencil of Fano double covers. III
• Birationally rigid complete intersections of quadrics and cubics
• Birationally rigid Fano cyclic covers
• Birationally rigid varieties with a pencil of Fano double covers. II
• Birational superrigidity is not a locally closed property
• Birational geometry of Fano double covers
• Birational superrigidity and slope stability of Fano manifolds
• Birationally rigid Fano complete intersections. II
• On nodal sextic fivefold
• Birational geometry of Fano double spaces of index two
• Double cubics and double quartics