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Article Dans Une Revue Mathematische Annalen Année : 2019

Some loci of rational cubic fourfolds

Résumé

In this paper we investigate the geography of some codimension two loci inside the moduli space of smooth cubic hypersurfaces in $\mathbb{P}^5$ and the rationality of their elements. In particular, we study the loci of cubics which contain a plane and another surface, whose ideal is generated by quadratic equations. This is the case of cubic and quartic scrolls and Veronese surfaces - and some of their degenerations. Using the fact that all degenerations of quartic scrolls in $\mathbb{P}^5$ contained in a smooth cubic hypersurface are surfaces with one apparent double point, we also show that every cubic hypersurface belonging to the divisor $\mathcal{C}_{14}$ in the moduli space is rational.
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hal-01145459 , version 1 (29-03-2024)

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Michele Bolognesi, Francesco Russo, Giovanni Staglianò. Some loci of rational cubic fourfolds. Mathematische Annalen, 2019, 373, pp.165-190. ⟨10.1007/s00208-018-1707-7⟩. ⟨hal-01145459⟩
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