Birational geometry of Fano double spaces of index two

2008/12/19 by Александр Валентинович Пухликов, Pukhlikov, Aleksandr
Mathematics · #14E05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0812.3863

openalex publication_date 2008/12/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study birational geometry of Fano varieties, realized as double covers σ\colon V→ \mathbb P^M, M≥ 5, branched over generic hypersurfaces W=W_2(M-1) of degree 2(M-1). We prove that the only structures of a rationally connected fiber space on V are the pencils-subsystems of the free linear system |-\frac12 K_V|. The groups of birational and biregular self-maps of the variety V coincide.

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