English

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 A5\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.

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}
}