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 whose general surface sections have negative Kodaira dimension. In particular, we prove that a variety of dimension 𝑛⩾3 whose general surface sections have negative Kodaira dimension is birationally equivalent to the product of a general surface section times ℙ𝑛−2 unless (possibly) if the variety is a cubic hypersurface.

On varieties whose general surface section has negative Kodaira dimension / Ciliberto, Ciro; Fontanari, Claudio. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 2024:(2024), pp. 1-22. [10.1002/mana.202300565]

On varieties whose general surface section has negative Kodaira dimension

Ciliberto, Ciro;Fontanari, Claudio
2024-01-01

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 whose general surface sections have negative Kodaira dimension. In particular, we prove that a variety of dimension 𝑛⩾3 whose general surface sections have negative Kodaira dimension is birationally equivalent to the product of a general surface section times ℙ𝑛−2 unless (possibly) if the variety is a cubic hypersurface.
2024
Ciliberto, Ciro; Fontanari, Claudio
On varieties whose general surface section has negative Kodaira dimension / Ciliberto, Ciro; Fontanari, Claudio. - In: MATHEMATISCHE NACHRICHTEN. - ISSN 0025-584X. - 2024:(2024), pp. 1-22. [10.1002/mana.202300565]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/408414
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