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Seminar

Informal Seminar:" Positivity of the relative canonical bundle and applications" April 01, 2009
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Location: MSRI: Simons Auditorium
Speaker(s) Dr. Georg Schumacher
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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.

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