Albert

# Hodge theory and Moduli

 dc.contributor.author Griffiths, Phillip dc.date.accessioned 2020-10-06T14:45:05Z dc.date.available 2020-10-06T14:45:05Z dc.identifier.uri https://hdl.handle.net/20.500.12111/7924 dc.description CRM/ISM Colloquium lecture given in Montreal, October 9, 2020. en_US dc.description.abstract The theory of moduli is an important and active area in algebraic geometry. For varieties of general type the existence of a moduli space $\mathcal{M}$ with a canonical completion $\bar{\mathcal{M}}$ has been proved by Koll\'ar/Shepard-Barron/Alexeev. Aside from the classical case of algebraic curves, very little is known about the structure of $\mathcal{M}$, especially it's boundary $\overline{\mathcal{M}} \diagdown\mathcal{M}$. The period mapping from Hodge theory provides a tool for studying these issues. en_US In this talk, we will discuss some aspects of this topic with emphasis on I-surfaces, which provide one of the first examples where the theory has been worked out in some detail. Particular notice will me made of how the extension data in the limiting mixed Hodge structures that arise from singular surfaces on the boundary of moduli may be used to guide the desingularization of that boundary. dc.language.iso en_US en_US dc.subject Hodge theory en_US dc.subject Moduli en_US dc.title Hodge theory and Moduli en_US dc.type Lecture/speech en_US
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