Negative curves on very general blow-ups of P²

2005/12/29 by Tommaso de Fernex, de Fernex, Tommaso · 1 citation
Mathematics · #14C20 #14J25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14C20 #msc:14J25

paper · pdf · doi:10.48550/arxiv.math/0512631

arxiv created 2005/12/29 · arxiv updated 2009/12/01

Abstract

A conjecture, related to the Nagata conjecture and the Segre-Harbourne-Gimigliano-Hirschowitz conjecture, states that every integral curve with negative self-intersection on the blow-up of ¶² at a set of points in very general position is a (-1)-curve. In this paper we verify this conjecture for all curves whose image on ¶² is a curve with a singularity of multiplicity two at one of the centers of the blow-up.

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• Integral Zariski decompositions on smooth projective surfaces II

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