We prove that the moduli space of cubic fourfolds contains a divisor whose general member has a unirational parametrization of degree 13. This result follows from a thorough study of the Hilbert scheme of rational scrolls and an explicit construction of examples. We also show that is uniruled.
"New cubic fourfolds with odd-degree unirational parametrizations." Algebra Number Theory 11 (7) 1597 - 1626, 2017. https://doi.org/10.2140/ant.2017.11.1597