We study the second fundamental form of the Siegel metric in A5 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.
The second fundamental form of the moduli space of cubic threefolds in A5 / E. Colombo, P. Frediani, J. Carlos Naranjo, G. Pietro Pirola. - In: ÉPIJOURNAL DE GÉOMÉTRIE ALGÉBRIQUE. - ISSN 2491-6765. - 2023:9 Special Issue(2023 Oct 27), pp. 13432.1-13432.24. [10.46298/epiga.2023.9962]
The second fundamental form of the moduli space of cubic threefolds in A5
E. ColomboPrimo
;
2023
Abstract
We study the second fundamental form of the Siegel metric in A5 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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