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

TL;DR

This paper develops an asymptotic method based on Dumnicki's algorithm to estimate lower bounds for Seshadri constants on the projective plane, successfully establishing a bound of 4/13 for ten points.

Contribution

It introduces an asymptotic version of Dumnicki's algorithm to analyze linear systems and Seshadri constants in algebraic geometry.

Findings

Proves a lower bound of 4/13 for Seshadri constants of 10 general points.

Develops an asymptotic approach to Dumnicki's algorithm for linear systems.

Enhances understanding of positivity properties in algebraic geometry.

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 $\mathbb{P}^2$.