Cubic fourfolds fibered in sextic del Pezzo surfaces

Abstract

We exhibit new examples of rational cubic fourfolds, parametrized by a countably infinite union of codimension-two subvarieties in the moduli space. Our examples are fibered in sextic del Pezzo surfaces over the projective plane; they are rational whenever the fibration has a rational section.

23 pages, Macaulay2 code as an ancillary file. final version to appear in Amer J Math

References in corpus (3)

• The K3 category of a cubic fourfold
• Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds
• Explicit rationality of some cubic fourfolds

Cited by in corpus (9)

• Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds
• Cycles, derived categories, and rationality
• Brill-Noether special cubic fourfolds of discriminant 14
• Relative linear extensions of sextic del Pezzo fibrations
• Rational fibered cubic fourfolds
• Rational cubic fourfolds in Hassett divisors
• Hodge numbers are not derived invariants in positive characteristic
• Rational cubic fourfolds with associated singular K3 surfaces
• Refinement of the classification of weak Fano threefolds with sextic del Pezzo fibrations