Speaker: Yilong Zhang
Date: 10:30 15/09/2023
Title: Periods of Cubic Surfaces
Abstract: A cubic surface has no holomorphic 2-form, so its cohomology does not carry an interesting
 Hodge structure. However, a 3-to-1 cover of P^3 branched along a cubic surface is a cubic threefold, 
 whose Hodge structure in H^3 is not trivial, and in fact determines the cubic threefold by a Torelli 
 theorem of Clemens and Griffiths. In this way, Allock, Carlson, and Toledo found a moduli space of cubic 
 surfaces, which is four-dimensional. We consider another four-dimensional family of cubic surfaces: the 
 hyperplane sections of a fixed cubic threefold X. There is a period map from (P^4)* to the moduli of cubic
  surfaces by sending a hyperplane H to X∩H. It is rational and dominant. We'd like to understand how this 
  map behaves near singular fibers and how it behaves globally. Part of the work is based on a joint work 
  with Lisa Marquand.