SINGLE POINT SESHADRI CONSTANTS ON RATIONAL SURFACES

Authors

Krishna Hanumanthu, Chennai Mathematical InstituteFollow
Brian Harbourne, University of Nebraska - LincolnFollow

Date of this Version

2017

Citation

Volume 499, 1 April 2018, Pages 37-42

Comments

Published in the Journal of Algebra

https://doi.org/10.1016/j.jalgebra.2017.11.040

Abstract

Motivated by a similar result of Dumnicki, Küronya, Maclean and Szemberg under a slightly stronger hypothesis, we exhibit irrational single-point Seshadri constants on a rational surface X obtained by blowing up very general points of P² _C, assuming only that all prime divisors on X of negative self-intersection are smooth rational curves C with C² = −1. (This assumption is a consequence of the SHGH Conjecture, but it is weaker than assuming the full conjecture.)