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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)
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Location: MSRI: Simons Auditorium
Speaker(s) Klaus Hulek (Universität Hannover)
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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.

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