Abstract
We propose a new construction which associates to any ample (or big) line bundle on a projective manifold a canonical growth condition (i.e., a choice of a plurisubharmonic (psh) function well defined up to a bounded term) on the tangent space of any given point . We prove that it encodes such classical invariants as the volume and the Seshadri constant. Even stronger, it allows one to recover all the infinitesimal Okounkov bodies of at . The construction is inspired by toric geometry and the theory of Okounkov bodies; 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. We prove a theorem about Kähler embeddings of large balls, which generalizes the well-known connection between Seshadri constants and Gromov width established by McDuff and Polterovich.
Citation
David Witt Nyström. "Canonical growth conditions associated to ample line bundles." Duke Math. J. 167 (3) 449 - 495, 15 February 2018. https://doi.org/10.1215/00127094-2017-0031
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