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Birational geometry of algebraic varieties, fibred into Fano double spaces by Pukhlikov, Aleksandr V. is a scholarly article available to read on EtoBox.

What is Birational geometry of algebraic varieties, fibred into Fano double spaces about?

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.

Author

Pukhlikov, Aleksandr V.

Published

2015

Language

EN