On the moduli space of pairs consisting of a cubic threefold and a hyperplane Academic Article uri icon

abstract

  • 2018 Elsevier Inc. We study the moduli space of pairs (X,H) consisting of a cubic threefold X and a hyperplane H in P4. The interest in this moduli comes from two sources: the study of certain weighted hypersurfaces whose middle cohomology admit Hodge structures of K3 type and, on the other hand, the study of the singularity O16 (the cone over a cubic surface). In this paper, we give a Hodge theoretic construction of the moduli space of cubic pairs by relating (X,H) to certain lattice polarized cubic fourfolds Y. A period map for the pairs (X,H) is then defined using the periods of the cubic fourfolds Y. The main result is that the period map induces an isomorphism between a GIT model for the pairs (X,H) and the BailyBorel compactification of some locally symmetric domain of type IV.

published proceedings

  • ADVANCES IN MATHEMATICS

author list (cited authors)

  • Laza, R., Pearlstein, G., & Zhang, Z.

citation count

  • 9

complete list of authors

  • Laza, Radu||Pearlstein, Gregory||Zhang, Zheng

publication date

  • January 2018