A note on special cubic fourfolds of discriminant 14 and non-minimal K3 surfaces of degree 10

2024/04/11 by Jordi Hernández, Hernández, Jordi
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2404.07891

openalex publication_date 2024/04/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that a general cubic in the Hassett divisor C₁₄ of special cubic fourfolds of discriminant 14 contains a non-minimal K3 surface of degree 10 containing two skew (-1)-lines and contained in a smooth quadric hypersurface Q⁴⊆ ℙ⁵, but not contained in any other (possibly of lower rank) quadric hypersurface.

Related

• Cubic fourfolds containing a plane and K3 surfaces of Picard rank two
• Rational cubic fourfolds with associated singular K3 surfaces
• Supporting rank and the intersection of all Hassett Divisors
• A nonspecial divisor in the moduli space of cubic fourfolds via 10-nodal plane sextics
• Variety of power sums and divisors in the moduli space of cubic fourfolds