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Sur un théorème de Catselnuovo

Pan, Yvan
Published in Bulletin of the Brazilian Mathematical Society. 2008, vol. 39, no. 1, p. 61-80
Abstract We continue the study of G. Castelnuovo on the group of birational transformations of the complex plane that fix each point of a curve of genus > 1 ; we use adjoint linear system of the curve as Castelnuovo does. We prove that these groups are abelian, and that these are either finite, of order 2 or 3, or conjuguate to a subgroup of the de Jonquières group. We show also that these results do not generalise to curves of genus ≤ 1.
Keywords Cremona transformationsBirational transformationsFixed curvesCurves of high genusAdjoint linear systemDe Jonquières transformations
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BLANC, Jeremy, PAN, Yvan, VUST, Thierry. Sur un théorème de Catselnuovo. In: Bulletin of the Brazilian Mathematical Society, 2008, vol. 39, n° 1, p. 61-80. doi: 10.1007/s00574-008-0072-7 https://archive-ouverte.unige.ch/unige:9771

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Deposited on : 2010-07-29

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