# Mathematical Sciences Research Institute

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# Seminar

BGMS Seminar: Moduli Spaces of Cubic Threefolds — Geometry and Topology February 14, 2019 (01:30 PM PST - 02:30 PM PST)
Parent Program: Birational Geometry and Moduli Spaces MSRI: Simons Auditorium
Speaker(s) Klaus Hulek (Universität Hannover)
Description No Description
Video
Cubic threefolds were the first class of varieties who were shown to be unirational but not rational (Clemens,Griffiths). The key tool of the proof is the intermediate Jacobian, a principally polarized abelian variety of dimension 5. There is a second link to Hodge theory, namely via cubic fourfolds (Allcock, Carlson, Toledo) which leads to a $10$-dimensional ball quotient model. Looking at cubic threefolds from these different points of view leads to various geometrically relevant compactifications of the moduli space of cubic threefolds. In this talk I will discuss the geometry and the topology of these spaces. This is joint work with S. Casalaina-Martin, S. Grushevsky and R. Laza.