Abstract
For every integer \(k \ge 3\) we describe a new family of foliations of degree k with one singularity. We show that a very generic member of this family has trivial isotropy group and a line as its unique Darboux polynomial.
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06 July 2020
We fix a mistake in the argument leading to the proof that the family of foliations introduced in the paper does not have an algebraic solution apart from the line at infinity
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Acknowledgements
During the preparation of the paper the first author was partially supported by CNPq Grant 304543/2017-9 and the second author by a Grant PIBIC(CNPq). We also benefited from the access to on-line journals provided by CAPES. We would also like to thank the referee for numerous suggestions that greatly improved this paper.
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Coutinho, S.C., Ferreira, F.R. A Family of Foliations with One Singularity. Bull Braz Math Soc, New Series 51, 957–974 (2020). https://doi.org/10.1007/s00574-019-00183-8
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DOI: https://doi.org/10.1007/s00574-019-00183-8