Generation of jets and Fujita’s jet ampleness conjecture on toric varieties

Abstract: A line bundle is k-jet ample if it has enough global sections to separate points, tangent vectors, and also their higher order analogues called k-jets. For example, 0-jet ampleness is equivalent to global generation and 1-jet ampleness is equivalent to very ampleness. We give sharp bounds guaranteeing that a line bundle on a projective toric variety is k-jet ample in terms of its intersection numbers with the invariant curves, in terms of the lattice lengths of the edges of its polytope, in terms of the higher concavity of its piecewise linear function and in terms of its Seshadri constant. As an application, we prove the k-jet generalizations of Fujita’s conjectures on toric varieties.

algebraic geometrynumber theory

Audience: researchers in the topic

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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