Frederic Campana (University of Lorraine, Nancy)
Title: Special manifolds and the Kobayashi pseudometric.
Abstract: If $X$ is a submanifold of an Abelian variety, the Ueno fibration $p:X\to Z$ turns $X$ into a bundle with fibres $B$, an Abelian subvariety of $A$, and $Z\subset A/B$, of general type. Let $d_X$ be the Kobayashi pseudodistance on $X$. Then $d_X=p^*(d_Z)$, and $d_Z$ is a metric generically on $Z$ by Lang's conjecture (solved here by K. Yamanoi).
The goal is to give a similar description for arbitrary projective $X$, using its `Core map' $c:X\to Z$, which has `special' fibres $X_z$, and `orbifold base' $(Z,D_c)$ of general type, so that its naturally defined Kobayashi pseudodistance should be generically a metric on $Z$ .Ìý$D_c$ is a divisor on $Z$, nonzero in general, which encodes the multiple fibres of $c$.Ìý$X_z$ `Special' means that $\Omega^p_{X_z}$ has no rank-one subsheaf of maximal Kodaira dimension $p$. They are conjecturally exactly the ones with $d_X\equiv 0$.
The talk will give the relevant definitions, and illustrate the conjecture by examples.
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Online meeting details:
Ìý
Link:
Reunion ID : 5132
PIN : 2680
N.B. Please note that this is not zoom and uses an University of Lorraine video conferencing software — It opens in an internet browser but has some compatibility problem with firefox and so one needs to avoid some browsers.