Cubic fourfolds fibered in sextic del Pezzo surfaces
Nicolas Addington, Brendan Hassett, Yuri Tschinkel, and Anthony, V\'arilly-Alvarado
TL;DR
This paper introduces new rational cubic fourfolds fibered in sextic del Pezzo surfaces, expanding the known examples and providing conditions for their rationality based on the existence of rational sections.
Contribution
It constructs infinitely many new rational cubic fourfolds fibered in sextic del Pezzo surfaces, characterized by specific subvarieties in the moduli space.
Findings
New examples of rational cubic fourfolds are constructed.
Rationality is achieved when the fibration admits a rational section.
Examples are parametrized by a countably infinite union of codimension-two subvarieties.
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.
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