On varieties whose general surface section has negative Kodaira dimension

Ciro Ciliberto and Claudio Fontanari

Mathematische Nachrichten, 2024, vol. 297, issue 8, 2927-2948

Abstract: In this paper, inspired by work of Fano, Morin, and Campana–Flenner, we give a projective classification of varieties of dimension 3 whose general hyperplane sections have negative Kodaira dimension, and we partly extend such a classification to varieties of dimension n⩾4$n\geqslant 4$ whose general surface sections have negative Kodaira dimension. In particular, we prove that a variety of dimension n⩾3$n\geqslant 3$ whose general surface sections have negative Kodaira dimension is birationally equivalent to the product of a general surface section times Pn−2${\mathbb {P}}^{n-2}$ unless (possibly) if the variety is a cubic hypersurface.

Date: 2024
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https://doi.org/10.1002/mana.202300565

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