Birationally rigid iterated Fano double covers

Details Birationally rigid iterated Fano double covers Birationally rigid iterated Fano double covers

2003-10-17

arxiv.org/abs/math/0310268v1

Izvestiya: Mathematics. 67 (2003), no. 3, 555-596

Mathematics

Algebraic Geometry

51 pages

Scientific paper

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.

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