Toric Newton-Okounkov functions with an application to the rationality of certain Seshadri constants on surfaces

Abstract

We initiate a combinatorial study of Newton-Okounkov functions on toric varieties with an eye on the rationality of asymptotic invariants of line bundles. In the course of our efforts we identify a combinatorial condition which ensures a controlled behavior of the appropriate Newton-Okounkov function on a toric surface. Our approach yields the rationality of many Seshadri constants that have not been settled before.

52 pages, 37 figures; significant revision of section 5

References in corpus (1)

• Functions on Okounkov bodies coming from geometric valuations (with an appendix by Sébastien Boucksom)

Cited by in corpus (1)

• On the finite generation of valuation semigroups on toric surfaces