2004/04/25 by Paolo Stellari, Stellari, Paolo · 1 citation
Mathematics · #14H50 #14J35 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research
paper · pdf · doi:10.48550/arxiv.math/0404448
openalex publication_date 2004/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we consider cubic 4-folds containing a plane whose discriminant curve is a reduced nodal plane sextic. In particular, we describe the singular points of such cubic 4-folds and we give an estimate of the rank of the free abelian group generated by the equivalence classes of the algebraic cycles of codimension 2. Moreover, we describe some conditions on the geometry of the plane sextics so that all the associated cubic 4-folds are singular and we construct a family of smooth rational cubic 4-folds whose discriminant curve is reduced but reducible.