Frobenius–Seshadri constants and characterizations of projective space

We introduce higher-order variants of the Frobenius–Seshadri constant due to Mustaţă and Schwede, which are defined for ample line bundles in positive characteristic. These constants are used to show that Demailly’s criterion for separation of higher-order jets by adjoint bundles also holds in positive characteristic. As an application, we give a characterization of projective space using Seshadri constants in positive characteristic, which was proved in characteristic zero by Bauer and Szemberg. We also discuss connections with other characterizations of projective space.

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This material is based upon work supported by the National Science Foundation under Grant No. DMS-1265256.

Received 20 January 2017

Accepted 7 August 2017

Published 3 August 2018