The second fundamental form of the moduli space of cubic threefolds in $\mathcal{A}

Colombo, ElisabettaFrediani, PaolaNaranjo del Val, Juan CarlosPirola, Gian Pietro2024-02-192024-02-192023-10-272491-6765https://hdl.handle.net/2445/207689We 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.24 p.application/pdfengcc-by-sa (c) Colombo, E. et al., 2023http://creativecommons.org/licenses/by-sa/4.0/Corbes algebraiquesFuncions de diverses variables complexesSuperfícies algebraiquesGeometria algebraicaAlgebraic curvesFunctions of several complex variablesAlgebraic surfacesAlgebraic geometryThe second fundamental form of the moduli space of cubic threefolds in $\mathcal{A}_5$info:eu-repo/semantics/article7361662024-02-19info:eu-repo/semantics/openAccess