# Geometric Analysis and Topology Seminar

#### Jumping of the Symmetric Plurigenera Along Families

Speaker: Bruno De Oliveira, Miami

Location: Warren Weaver Hall 813

Date: Friday, October 13, 2006, 11 a.m.

Synopsis:

We give new results and examples about the jump along smooth families of projective varieties $$X_t$$ of the symmetric plurigenera, $$Q_m(X) = \dim H^0 (X, S^m \Omega^1_X)$$ (and also of $$\alpha$$-twisted symmetric plurigenera, $$Q_{\alpha,m}(X) = \dim H^0 (X, S^m (\Omega^1_X \otimes \alpha K_X))$$. We will present and use new results about the space of twisted symmetric differentials on subvarieties $$X$$ of $$\mathbb{P}^N$$ with $$\dim X \geq 2/3N$$.