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arXiv · 2207.13432

The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$

Elisabetta Colombo·Paola Frediani·Juan Carlos Naranjo·Gian Pietro Pirola
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Abstract

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.

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Elisabetta Colombo, Paola Frediani, Juan Carlos Naranjo, Gian Pietro Pirola. 2022-07-27. The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$. https://doi.org/10.46298/epiga.2023.9962

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