Birational geometry of Fano double spaces of index two

Abstract

We study birational geometry of Fano varieties, realized as double covers $\sigma :V\to {\mathbb{P}}^M$, $M\ge 5$, 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 $|-\frac{1}{2}{K}_V|$. The groups of birational and biregular self-maps of the variety $V$ coincide.

LaTeX, 77 pages

References in corpus (3)

• Log canonical thresholds of certain Fano hypersurfaces
• Birational rigidity is not an open property
• On the $8n^2$-inequality