Duke Mathematical Journal
- Duke Math. J.
- Volume 167, Number 3 (2018), 449-495.
Canonical growth conditions associated to ample line bundles
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.
Duke Math. J., Volume 167, Number 3 (2018), 449-495.
Received: 7 October 2015
Revised: 24 June 2017
First available in Project Euclid: 5 January 2018
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Witt Nyström, David. Canonical growth conditions associated to ample line bundles. Duke Math. J. 167 (2018), no. 3, 449--495. doi:10.1215/00127094-2017-0031. https://projecteuclid.org/euclid.dmj/1515143006