Normal subgroups in the Cremona group

被引：56

作者：

Cantat, Serge ^{[1
]}

Lamy, Stephane ^{[2
]}

de Cornulier, Yves ^{[3
,4
]}

机构：

[1] Univ Rennes 1, FR-35042 Rennes, France

[2] Univ Warwick, Math Inst, Coventry CV4 7AL, W Midlands, England

[3] CNRS, FR-91405 Orsay, France

[4] Univ Paris 11, Lab Math Orsay, FR-91405 Orsay, France

来源：

ACTA MATHEMATICA | 2013年 / 210卷 / 01期

关键词：

AUTOMORPHISMS;

D O I：

10.1007/s11511-013-0090-1

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory and algebraic geometry to produce elements in the Cremona group that generate non-trivial normal subgroups.

引用

页码：31 / 94

页数：64

共 50 条

[1] The Cremona group and its subgroups
Dolgachev, Igor
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2022,
[2] The Cremona group and its subgroups
Dolgachev, Igor
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 2022, 59 (04) : 617 - 622
[3] Nilpotent subgroups of the Cremona group
Deserti, Julie
BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, 2007, 38 (03): : 377 - 388
[4] Subgroups of elliptic elements of the Cremona group
Urech, Christian
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2021, 770 : 27 - 57
[5] Finite subgroups of the plane Cremona group
Dolgachev, Igor V.
ALGEBRAIC GEOMETRY IN EAST ASIA - SEOUL 2008, 2010, 60 : 1 - 49
[6] Borel subgroups of the plane Cremona group
Furter, Jean-Philippe
Heden, Isac
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 2023, 2023 (794): : 133 - 177
[7] Finite Abelian subgroups of the Cremona group of the plane
Blanc, Jeremy
COMPTES RENDUS MATHEMATIQUE, 2007, 344 (01) : 21 - 26
[8] p-Elementary subgroups of the Cremona group
Beauville, Arnaud
JOURNAL OF ALGEBRA, 2007, 314 (02) : 553 - 564
[9] INFINITE ALGEBRAIC SUBGROUPS OF THE REAL CREMONA GROUP
Robayo, Maria Fernanda
Zimmermann, Susanna
OSAKA JOURNAL OF MATHEMATICS, 2018, 55 (04) : 681 - 712
[10] p-subgroups in the space Cremona group
Prokhorov, Yuri
Shramov, Constantin
MATHEMATISCHE NACHRICHTEN, 2018, 291 (8-9) : 1374 - 1389

← 1 2 3 4 5 →