Birational geometry of Fano double spaces of index two

Details Birational geometry of Fano double spaces of index two Birational geometry of Fano double spaces of index two

2008-12-19

arxiv.org/abs/0812.3863v2

Mathematics

Algebraic Geometry

LaTeX, 77 pages

Scientific paper

We study birational geometry of Fano varieties, realized as double covers $\sigma\colon V\to {\mathbb P}^M$, $M\geq 5$, 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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