Negative curves on very general blow-ups of P^2

Tommaso de Fernex

Negative curves on very general blow-ups of P^2

Algebraic Geometry 2007-05-23 v1

Authors: Tommaso de Fernex

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 $\P^2$ 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 $\P^2$ is a curve with a singularity of multiplicity two at one of the centers of the blow-up.

Keywords

negative curves blow-up of P^2 very general position (-1)-curve Nagata conjecture SHGH conjecture

Cite

@article{arxiv.math/0512631,
  title  = {Negative curves on very general blow-ups of P^2},
  author = {Tommaso de Fernex},
  journal= {arXiv preprint arXiv:math/0512631},
  year   = {2007}
}

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