Geodesic
The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$
Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023)

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We study the second fundamental form of the Siegel metric in $\mathcal A_5$ restricted to the locus of intermediate Jacobians of cubic threefolds. We prove that the image of this second fundamental form, which is known to be non-trivial, is contained in the kernel of a suitable multiplication map. Some ingredients are: the conic bundle structure of cubic threefolds, Prym theory, Gaussian maps and Jacobian ideals.
DOI : 10.46298/epiga.2023.9962
Classification : 14H40, 14J10, 14J70, 32G20 
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     author = {Colombo, Elisabetta and Frediani, Paola and Naranjo, Juan Carlos and Pirola, Gian Pietro},
     title = {The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     year = {2023},
     doi = {10.46298/epiga.2023.9962},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.9962/}
}
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Colombo, Elisabetta; Frediani, Paola; Naranjo, Juan Carlos; Pirola, Gian Pietro. The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$. Épijournal de Géométrie Algébrique, Special volume in honour of Claire Voisin (2023). doi: 10.46298/epiga.2023.9962

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