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arXiv · 1707.00999

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

Francesco Russo·Giovanni Staglianò
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Abstract

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.

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Francesco Russo, Giovanni Staglianò. 2017-07-04. Congruences of 5-secant conics and the rationality of some admissible cubic fourfolds. https://doi.org/10.1215/00127094-2018-0053

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