Moduli and Hodge Theory |
| Phillip Griffiths |
| Institute for Advanced Studies, Princeton (USA) |
| Abstract: |
| Moduli spaces of varieties \[X\] are of central interest in algebraic geometry. For \[X\] smooth and of general type the moduli space \[\it M\] exists and has a canonical projective completion \[\overline{\it M}\] . Aside from the case of algebraic curves there are essentially no general results about or examples of the structure of the boundary \[\overline{\it M}\setminus {\it M}\] . |
| 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 \[\overline{\it M}\setminus {\it M}\] . 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. |