Birational geometry of Fano double spaces of index two

作者：Pukhlikov A V^*

来源：Izvestiya - Mathematics, 2010, 74(5): 925-991.

DOI：10.1070/IM2010v074n05ABEH002512

• birational map
• Fano variety
• maximal singularity
• rationally connected fibre space
• birational self-map

We study birational geometry of Fano varieties realized as double covers sigma: V -> P(M), M >= 5, branched over generic smooth hypersurfaces 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 vertical bar-1/2K(v)vertical bar. The groups of birational and biregular self-maps of V coincide: Bir V = Aut V.

• 出版日期2010-10