The number of conjugacy classes of elements of the Cremona group of some given finite order

Jérémy Blanc

Bulletin de la Société Mathématique de France (2007)

  • Volume: 135, Issue: 3, page 419-434
  • ISSN: 0037-9484

Abstract

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This note presents the study of the conjugacy classes of elements of some given finite order n in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if n is even, n = 3 or n = 5 , and that it is equal to 3 (respectively 9 ) if n = 9 (respectively if n = 15 ) and to 1 for all remaining odd orders. Some precise representative elements of the classes are given.

How to cite

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Blanc, Jérémy. "The number of conjugacy classes of elements of the Cremona group of some given finite order." Bulletin de la Société Mathématique de France 135.3 (2007): 419-434. <http://eudml.org/doc/272315>.

@article{Blanc2007,
abstract = {This note presents the study of the conjugacy classes of elements of some given finite order $n$ in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if $n$ is even, $n=3$ or $n=5$, and that it is equal to $3$ (respectively $9$) if $n=9$ (respectively if $n=15$) and to $1$ for all remaining odd orders. Some precise representative elements of the classes are given.},
author = {Blanc, Jérémy},
journal = {Bulletin de la Société Mathématique de France},
keywords = {Cremona group; birational transformations; conjugacy classes; elements of finite order},
language = {eng},
number = {3},
pages = {419-434},
publisher = {Société mathématique de France},
title = {The number of conjugacy classes of elements of the Cremona group of some given finite order},
url = {http://eudml.org/doc/272315},
volume = {135},
year = {2007},
}

TY - JOUR
AU - Blanc, Jérémy
TI - The number of conjugacy classes of elements of the Cremona group of some given finite order
JO - Bulletin de la Société Mathématique de France
PY - 2007
PB - Société mathématique de France
VL - 135
IS - 3
SP - 419
EP - 434
AB - This note presents the study of the conjugacy classes of elements of some given finite order $n$ in the Cremona group of the plane. In particular, it is shown that the number of conjugacy classes is infinite if $n$ is even, $n=3$ or $n=5$, and that it is equal to $3$ (respectively $9$) if $n=9$ (respectively if $n=15$) and to $1$ for all remaining odd orders. Some precise representative elements of the classes are given.
LA - eng
KW - Cremona group; birational transformations; conjugacy classes; elements of finite order
UR - http://eudml.org/doc/272315
ER -

References

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  13. [13] J. Kollár – Rational curves on algebraic varieties, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics, vol. 32, Springer, 1996. Zbl0877.14012MR1440180
  14. [14] Y. Manin – « Rational surfaces over perfect fields, II », Math. USSR Sbornik1 (1967), p. 141–168. Zbl0182.23701
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