Elisabetta Colombo ; Paola Frediani ; Juan Carlos Naranjo ; Gian Pietro Pirola - The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$

epiga:9962 - Épijournal de Géométrie Algébrique, October 27, 2023, Special volume in honour of Claire Voisin - https://doi.org/10.46298/epiga.2023.9962
The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$Article

Authors: Elisabetta Colombo ; Paola Frediani ; Juan Carlos Naranjo ; Gian Pietro Pirola

    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.


    Volume: Special volume in honour of Claire Voisin
    Published on: October 27, 2023
    Accepted on: July 31, 2023
    Submitted on: August 24, 2022
    Keywords: Mathematics - Algebraic Geometry,14J30, 14J10, 32G20, 14H40

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