# 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}
}
• Published 2012
• Mathematics
• The Journal of Geometric Analysis
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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