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
公開日: 2022/7/27
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.