Irrational nef rays at the boundary of the Mori cone for very general blowups of the plane

TL;DR

This paper introduces a new technique to identify irrational rays at the boundary of the Mori cone in blowups of the plane, providing examples of such rays, which are non-effective and irrational.

Contribution

Develops a novel method for discovering irrational boundary rays of the Mori cone in general plane blowups, with explicit examples.

Findings

Identified non-effective irrational rays at the Mori cone boundary.

Developed a technique applicable to general blowups of the plane.

Provided explicit examples of irrational rays.

Abstract

In this paper we develop a technique for discovering (non-effective) irrational rays at the boundary of the Mori cone for linear systems on a general blowup of the plane, and give examples of such irrational rays.