Curves generating extremal rays in blowups of weighted projective planes

@article{GonzalezAnaya2020CurvesGE,
  title={Curves generating extremal rays in blowups of weighted projective planes},
  author={Javier Gonz'alez-Anaya and Jos{\'e} Luis Gonz{\'a}lez and Kalle Karu},
  journal={Journal of the London Mathematical Society},
  year={2020},
  volume={104}
}
We consider blowups at a general point of weighted projective planes and, more generally, of toric surfaces with Picard number 1. We give a unifying construction of negative curves on these blowups such that all previously known families appear as boundary cases of this. The classification consists of two classes of said curves, each depending on two parameters. Every curve in these two classes is algebraically related to other curves in both classes; this allows us to find their defining… 
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