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Scientific article
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English

Sur un théorème de Catselnuovo

Published inBulletin Brazilian Mathematical Society, vol. 39, no. 1, p. 61-80
Publication date2008
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 transformations
  • Birational transformations
  • Fixed curves
  • Curves of high genus
  • Adjoint linear system
  • De Jonquières transformations
Classification
  • arxiv : math.AG
Citation (ISO format)
BLANC, Jeremy, PAN, Yvan, VUST, Thierry. Sur un théorème de Catselnuovo. In: Bulletin Brazilian Mathematical Society, 2008, vol. 39, n° 1, p. 61–80. doi: 10.1007/s00574-008-0072-7
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ISSN of the journal1678-7544
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