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On the Moduli Space of Pairs Consisting of a Cubic Threefold and a Hyperplane by Laza, Radu; Pearlstein, Gregory; Zhang, Zheng is a scholarly article available to read on EtoBox.

What is On the Moduli Space of Pairs Consisting of a Cubic Threefold and a Hyperplane about?

We study the moduli space of pairs $(X,H)$ consisting of a cubic threefold $X$ and a hyperplane $H$ in $\mathbb P^4$. 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 $O_{16}$ (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 Baily-Borel compactification of some locally symmetric domain of type IV.

Author

Laza, Radu; Pearlstein, Gregory; Zhang, Zheng

Published

2017

Language

EN