On varieties whose general surface section has negative Kodaira dimension

2023/05/15 by Ciliberto, Ciro, Fontanari, Claudio
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2305.08730

Abstract

In this paper, inspired by work of Fano, Morin and Campana--Flenner, we give a full projective classification of (however singular) 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 \p^n-2 unless (possibly) if the variety is a cubic hypersurface.

Related

• Birational positivity in dimension 4 (with an appendix by Frédéric Campana)
• Varieties with pseudoeffective canonical divisor and their Kodaira dimension
• Conjectures on the Kodaira dimension
• Elliptic fibrations and Kodaira dimensions of Schreieder's varieties
• Mukai models and Borcherds products