Hodge theory and Moduli

Show simple item record Griffiths, Phillip 2020-10-06T14:45:05Z 2020-10-06T14:45:05Z
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. 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. en_US
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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