Non effective planar linear systems at the boundary of the Mori cone

TL;DR

This paper demonstrates that specific linear systems of plane curves with general base points and zero self-intersection are empty, providing new examples of boundary rays of the Mori cone for blow-ups of the plane.

Contribution

It introduces new instances of boundary rays of the Mori cone by proving the emptiness of certain linear systems with particular properties.

Findings

Linear systems with zero self-intersection are empty

Examples of boundary rays of the Mori cone are expanded

All multiples of these linear systems are also empty

Abstract

In this paper we prove that certain linear systems (and all their multiples) of plane curves with general base points and zero--self intersection are empty, thus exhibiting further examples of rays at the boundary of the Mori cone of a general blow--up of the plane.