Emptiness of homogeneous linear systems with ten general base points

TL;DR

This paper provides a new proof that certain linear systems of plane curves with ten general base points are empty when the degree-to-multiplicity ratio is below 117/37, advancing understanding in algebraic geometry.

Contribution

It introduces a novel proof establishing emptiness of these linear systems for a specific ratio, refining previous results in algebraic geometry.

Findings

Linear systems with ten general base points are empty if d/m < 117/37

New proof technique for emptiness of linear systems

Improved bounds for the non-existence of certain plane curves

Abstract

In this paper we give a new proof of the fact that for all pairs of positive integers (d, m) with d/m < 117/37, the linear system of plane curves of degree d with ten general base points of multiplicity m is empty.