An asymptotic version of Dumnicki's algorithm for linear systems in ${\mathbb{CP}}^2$

Abstract

Using Dumnicki's approach to showing non-specialty of linear systems consisting of plane curves with prescribed multiplicities in sufficiently general points on ${\mathbb{P}}^2$ we develop an asymptotic method to determine lower bounds for Seshadri constants of general points on ${\mathbb{P}}^2$. With this method we prove the lower bound 4/13 for 10 general points on ${\mathbb{P}}^2$.

14 pages, 5 figures, references added