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arXiv · 1712.08796

Birational geometry of singular Fano hypersurfaces of index two

Aleksandr V. Pukhlikov
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Abstract

For a Zariski general (regular) hypersurface $V$ of degree $M$ in the $(M+1)$-dimensional projective space, where $M$ is at least 16, with at most quadratic singularities of rank at least 13, we give a complete description of the structures of rationally connected (or Fano-Mori) fibre space: every such structure over a positive-dimensional base is a pencil of hyperplane sections. This implies, in particular, that $V$ is non-rational and its groups of birational and biregular automorphisms coincide. The set of non-regular hypersurfaces has codimension at least $\frac12(M-11)(M-10)-10$ in the natural parameter space.

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BibTeXRIS

Aleksandr V. Pukhlikov. 2017-12-23. Birational geometry of singular Fano hypersurfaces of index two. https://arxiv.org/abs/1712.08796

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