GVA Colloquium on Algebraic Geometry


January 26 2006,
Department of Mathematics, University of Milano

On the image of a period map that is an open embedding
Eduard J.N. Looijenga
(Universiteit Utrecht)

The following statement results from combining the work of many people: The period map for certain hypersurfaces, among them divisors of degree 8 or 12 on the projective line, cubic, quartic and sextic plane curves, cubic and quartic surfaces, cubic threefolds, cubic fourfolds, has the property that it embeds the moduli space of stable such hypersurfaces as an open subset in a symmetric domain (a complex ball or a type IV domain) modulo an arithmetic group. In most cases this embedding is strict. We describe a general and effective method for finding the complement of this embedding in such cases. We illustrate this with an example that was already well understood (quartic curves) and an example where this was not so (cubic threefolds). This represents joint work with Rogier Swierstra.

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