Growth conditions associated to ample (or big) line bundles

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Date(s) - 21/09/2015
14 h 00 min - 15 h 00 min

Catégories Pas de Catégories

I will discuss a new construction which associates to any ample (or big) line bundle on a projective manifold a canonical growth condition (i.e. an equivalence class of psh functions with bounded differences) on the tangent space of any given point. The canonical growth condition can be seen to encode such classical invariants as the volume and the Seshadri constant. It is inspired by toric geometry, and in fact in the toric case the growth condition is “equivalent” to the moment polytope. As in the toric case the growth condition says a lot about the Kähler geometry of the manifold. I will present a theorem about Kähler embeddings of large balls, which generalizes the connection between Seshadri constants and Gromov width established by McDuff and Polterovich.


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