The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$
Algebraic Geometry
2026-05-27 v3
Abstract
We study the second fundamental form of the Siegel metric in 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.
Keywords
Cite
@article{arxiv.2207.13432,
title = {The second fundamental form of the moduli space of cubic threefolds in $\mathcal A_5$},
author = {Elisabetta Colombo and Paola Frediani and Juan Carlos Naranjo and Gian Pietro Pirola},
journal= {arXiv preprint arXiv:2207.13432},
year = {2026}
}