Seshadri constants via Okounkov functions and the Segre-Harbourne-Gimigliano-Hirschowitz Conjecture

Abstract

In this note we relate the SHGH Conjecture to the rationality of one-point Seshadri constants on blow ups of the projective plane, and explain how rationality of Seshadri constants can be tested with the help of functions on Newton--Okounkov bodies.

13 pages

References in corpus (2)

• Variations on Nagata's Conjecture
• Functions on Okounkov bodies coming from geometric valuations (with an appendix by Sébastien Boucksom)

Cited by in corpus (1)

• Iterative dissection of Okounkov bodies of graded linear series on ${\mathbb{CP}}^2$