Birationally rigid hypersurfaces with quadratic singularities of low rank

A. V. Pukhlikov

Sbornik. Mathematics, Tome 215 (2024) no. 6, pp. 823-840

Résumé

It is shown that hypersurfaces of degree $M$ in ${\mathbb P}^M$, $M\geqslant 5$, with at most quadratic singularities of rank at least $3$ that satisfy certain conditions of general position are birationally superrigid Fano varieties and for $M\geqslant 8$ the complement to the set of such hypersurfaces is of codimension at least $\binom{M-1}{2} + 1$ with respect to the natural parameter space. Bibliography: 18 titles.

Détail

Keywords: Fano variety, birational rigidity, quadratic singularity.

Bibliographie

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