Some loci of rational cubic fourfolds

@article{Bolognesi2015SomeLO,
  title={Some loci of rational cubic fourfolds},
  author={M. Bolognesi and F. Russo and Giovanni Staglian{\`o}},
  journal={Mathematische Annalen},
  year={2015},
  volume={373},
  pages={165-190}
}
In this paper we investigate the divisor $${\mathcal {C}}_{14}$$C14 inside the moduli space of smooth cubic hypersurfaces in $${\mathbb {P}}^5$$P5, whose general element is a smooth cubic containing a smooth quartic rational normal scroll. By showing that all degenerations of quartic scrolls in $${\mathbb {P}}^5$$P5 contained in a smooth cubic hypersurface are surfaces with one apparent double point, we prove that every cubic hypersurface contained in $${\mathcal {C}}_{14}$$C14 is rational… Expand