Single point Seshadri constants on rational surfaces

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 ${\mathbb{P}}_{\mathbb{C}}^2$, assuming only that all prime divisors on $X$ of negative self-intersection are smooth rational curves $C$ with $C^2=-1$. (This assumption is a consequence of the SHGH Conjecture, but it is weaker than assuming the full conjecture.)

5 pages; minor changes since the original submission (additional references, slightly re-written introduction and proofs); to appear in J. Algebra