Seminar| Institute of Mathematical Sciences
Time：Friday, September 3rd, 2021, 15:00-16:00
Speaker: Zheng Zhang, ShanghaiTech University
Abstract:We study the moduli space of pairs consisting of a smooth cubic surface and a transverse plane via a period map. More specifically, the construction associates to a cubic surface pair a so-called Eckardt cubic threefold which admits an involution, and the period map sends the pair to the anti-invariant part of the intermediate Jacobian. Our main result is that the global Torelli theorem holds for the period map (in other words, the period map is injective). The key ingredients of the proof include a description of the anti-invariant part of the intermediate Jacobian as a Prym variety of a branched cover and a detailed study of certain positive dimensional fibers of the corresponding Prym map. This is joint work with S. Casalaina-Martin.