Departmental Colloquium
Phillip Griffiths
Institute for Advanced Study
Moduli and Hodge Theory
Abstract:
Moduli spaces of varieties X are of central interest in algebraic geometry.
For $X$ smooth and of general type the moduli space $M$ exists and has a canonical projective completion $\overline{M}$.
Aside from the case of algebraic curves there are essentially no general results about or examples of the structure of the boundary $\overline{M} \setminus M$.
Hodge theory provides the basic invariant of a complex algebraic variety.
Using Lie theory the space of Hodge structures and its boundary is well understood.
It is therefore natural to use the Hodge- theoretic boundary to study $\overline{M}\setminus M$. This talk will give an informal presentation of this approach together with one result and one application to moduli of a particularly interesting algebraic surface.
*Based on joint work in progress with Mark Green, Radu Laza, and Colleen Robles.
Friday April 5, 2019 at 3:00 PM in 636 SEO