On Plane Cremona Transformations of Fixed Degree

@article{Bisi2012OnPC,
  title={On Plane Cremona Transformations of Fixed Degree},
  author={Cinzia Bisi and Alberto Calabri and Massimiliano Mella},
  journal={The Journal of Geometric Analysis},
  year={2012},
  volume={25},
  pages={1108-1131}
}
We study the quasi-projective variety $\operatorname{Bir}_{d}$ of plane Cremona transformations defined by three polynomials of fixed degree d and its subvariety $\operatorname{Bir}_{d}^{\circ}$ where the three polynomials have no common factor. We compute their dimension and the decomposition in irreducible components. We prove that $\operatorname{Bir}_{d}$ is connected for each d and $\operatorname{Bir}_{d}^{\circ}$ is connected when d<7. 
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