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Negative curves on ${\bf P}^2$ Harbourne, Brian

Description

Consider a plane curve of degree d with points $p_1,\ldots,p_s$ of multiplicities $m_1=mult_{p_1}(C),\ldots,m_s=mult_{p_s}(C)$. Define $Q(C,p_1,\ldots,p_s)$ to be $d^2-\sum_im_i^2$ and say that $C$ is negative curve of $Q<0$. A well known conjecture states that there are no integral plane curves $C$ with $Q(C,p_1,\ldots,p_s)

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