Geometric Analysis and Topology Seminar

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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 \(\dim X \geq 2/3N\).