Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds

By Francesco Russo, Giovanni Staglianò. Duke mathematical journal, 2017

51 citations recorded by the source corpus.

The works of Hassett and Kuznetsov identify countably many divisors $C_d$ in the open subset of $\mathbb{P}^{55}=\mathbb{P}(H^0(\mathcal{O}_{\mathbb{P}^5}(3)))$ parametrizing all cubic 4-folds and conjecture that the cubics corresponding to these divisors are precisely the rational ones. Rationality has been known classically for the first family $C_{14}$. We use congruences of 5-secant conics to prove rationality for the first three of the families $C_d$, corresponding to $d=14, 26, 38$ in Hassett's notation.

Subfields: Algebra and Number Theory, Discrete Mathematics and Combinatorics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/8f8fc8b32fd4ab92f155199b3eced4cc26f209be