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

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

2005-12-29

arxiv.org/abs/math/0512631v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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