Birational geometry of Fano double spaces of index two

摘要

We study birational geometry of Fano varieties realized as double covers σ: V → ?M~M, M ≥ 5, branched over generic smooth hypersur-faces W = W_(2(M-1)) of degree 2(M - 1). We prove that the only structures of a rationally connected fibre space on V are pencil-subsystems of the free linear system | - 1/2 K_V |. The groups of birational and biregular self-maps of V coincide: Bir V = Aut V.