KTH/SU Mathematics
Colloquium
2 November
2005
Bo Berndtsson,
Chalmers
Curvature properties of
Bergman spaces
A Bergman
space is a space of holomorphic functions that are square integrable
over a domain with respect to some weight function. We will consider
Bergman spaces that in a sense depend holomorphically on a parameter,
so that the whole family of spaces defines a vector bundle over the
parameter space. The main theorem is a criterium for when such a
vector bundle is positively curved. We will also discuss analogs of
this result for Bergman spaces of holomorphic sections to line
bundles over compact manifolds and give several applications,
seemingly unconnected to Bergman spaces.