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 \({\frac{4}{13}}\) for 10 general points on \({\mathbb{P}^2}\).