Year of Graduation
Modular Forms and Cubics Surfaces
The moduli space of cubic surfaces has the description as the factor of the $4$-dimensional holomorphic ball by some discrete subgroup, but the explicit description of the corresponding periods map is known only in two examples. In this paper, we give the explicit construction of the moduli space for $1$-dimensional family of cubic surfaces that have the automorphism group $\left(\mathbb Z/3\mathbb Z \right)^2 \ltimes S_3$ and relate it to the classical modular curve $X_0(3)$. It gives the solution to one of the problems (from "Cubic surfaces with special periods" by Carlson and Toledo) of finding the explicit formula for periods of cubic surfaces that are a cyclic covering of the projective plane branched in a cubic curve.