Birational Geometry of Algebraic Varieties with a Pencil of Fano Cyclic Covers

We prove birational rigidity of fiber spaces pi : V -> P-1, the fiber of which is a Fano cyclic cover of index 1, provided it is sufficiently twisted over the base. In particular, non-rationality of these varieties is shown and their group of birational automorphisms is computed. The proof is obtained by a combination of the classical quadratic technique of the method of maximal singularities with the technique of hypertangent divisors and the connectedness principle of Shokurov and Kollar.