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arXiv · 0812.3863

Birational geometry of Fano double spaces of index two

Aleksandr Pukhlikov
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Abstract

We study birational geometry of Fano varieties, realized as double covers $σ\colon V\to {\mathbb P}^M$, $M\geq 5$, 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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Aleksandr Pukhlikov. 2009-05-22. Birational geometry of Fano double spaces of index two. https://arxiv.org/abs/0812.3863

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