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arXiv · 1512.05681

Birational geometry of algebraic varieties, fibred into Fano double spaces

Aleksandr V. Pukhlikov
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Abstract

We develop the quadratic technique of proving birational rigidity of Fano-Mori fibre spaces over a higher-dimensional base. As an application, we prove birational rigidity of generic fibrations into Fano double spaces of dimension $M\geqslant 4$ and index one over a rationally connected base of dimension at most $\frac12 (M-2)(M-1)$. An estimate for the codimension of the subset of hypersurfaces of a given degree in the projective space with a positive-dimensional singular set is obtained, which is close to the optimal one.

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Aleksandr V. Pukhlikov. 2017-12-14. Birational geometry of algebraic varieties, fibred into Fano double spaces. https://arxiv.org/abs/1512.05681

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