Frobenius-Seshadri constants and characterizations of projective space
arXiv:1701.00511 · doi:10.4310/MRL.2018.v25.n3.a9
Abstract
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.
19 pages. v2: Remark 3.3 added to discuss singularities, Propositions 2.8 and 2.11 added, references added, other small changes. v3: Fixed diagram on p. 16, other small changes
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