Cubic fourfolds fibered in sextic del Pezzo surfaces
  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. 
Nicolas Addington, Brendan Hassett, Yuri Tschinkel, and Anthony   V\'arilly-Alvarado
math.AG