Examples of non--effective rays at the boundary of the Mori cone of blow--ups of the plane

Abstract

In this paper we prove that no multiple of the linear system of plane curves of degree $d\ge 4$ with a point of multiplicity $d-m$ (with $2\le m\le d$) and $m(2d-m)$ simple general points is effective.

arXiv commentThis paper is dedicated to Giorgio Ottaviani on his 60th birthday