Blanc, Jérémy; Pan, Ivan; Vust, Thierry On a theorem of Castelnuovo. (Sur un théorème de Castelnuovo.) (French) Zbl 1139.14014 Bull. Braz. Math. Soc. (N.S.) 39, No. 1, 61-80 (2008). A birational map of the projective plane is called a Cremona transformation. If it preserves a pencil of lines, it is callled de Jonquières. The authors prove that \(F\) is a Cremona transformation which fixes point-wise an irreducible curve of genus \(>1\), then either \(F\) is conjugate (in the Cremona group) to a de Jonquières transformation or it is of order 2 or 3. A slightly weaker version was proved by G. Castelnuovo [Rom. Acc. L. Rend. (5) I, No. 1, 47–50 (1892; JFM 24.0577.03); or see J. L. Coolidge, A treatise on algebraic plane curves, Dover (1959; Zbl 0085.36403)]. Reviewer: N. Mohan Kumar (St. Louis) Cited in 1 ReviewCited in 7 Documents MSC: 14E07 Birational automorphisms, Cremona group and generalizations 14J26 Rational and ruled surfaces 14H50 Plane and space curves Keywords:Cremona transformations; de Jonquieres transformation; adjoint linear systems Citations:Zbl 0085.36403; JFM 24.0577.03 PDFBibTeX XMLCite \textit{J. Blanc} et al., Bull. Braz. Math. Soc. (N.S.) 39, No. 1, 61--80 (2008; Zbl 1139.14014) Full Text: DOI arXiv