Informal Seminar:" Positivity of the relative canonical bundle and applications"
Wed, April 1, 2009 11:00AM - 12:00PM
| Time: | 11:00AM - 12:00PM |
| Location: | Simons Auditorium |
| Speakers: | Georg Schumacher, Dr. Georg Schumacher |
| Abstract: | Given a family of canonically polarized manifolds, the Kaehler-Einstein metrics on the fiber define a hermitian metric on the relative canonical bundle. We show that this metric is strictly positive, if the family is effective. Furthermore, for degenerating such families, we get a singular hermitian metric. For a suitable compactification of the Hilbert scheme the determinant line bundle can be extended together with the Quillen metric, which also extends as a singular (semi-)positive hermitian metric. Applications concern hyperbolicity properties for moduli spaces and an analytic proof for the quasi-projectivity of the moduli space of canonically polarized varieties. |
