Normal subgroups in the Cremona group
Identifieur interne : 000061 ( Main/Exploration ); précédent : 000060; suivant : 000062Normal subgroups in the Cremona group
Auteurs : Serge Cantat [France] ; Stéphane Lamy [Royaume-Uni, France] ; Yves De Cornulier [France]Source :
- Acta Mathematica [ 0001-5962 ] ; 2013-03-01.
Abstract
Abstract: Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane $$ \mathbb{P}_{\mathbf{k}}^2 $$ 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.
Url:
DOI: 10.1007/s11511-013-0090-1
Affiliations:
- France, Royaume-Uni
- Midi-Pyrénées, Occitanie (région administrative), Région Bretagne, Île-de-France
- Paris, Rennes, Toulouse
- Université Toulouse III - Paul Sabatier, Université de Rennes 1
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We show that the Cremona group of all birational transformations of the projective plane $$ \mathbb{P}_{\mathbf{k}}^2 $$ 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.</div></front></TEI><affiliations><list><country><li>France</li><li>Royaume-Uni</li></country><region><li>Midi-Pyrénées</li><li>Occitanie (région administrative)</li><li>Région Bretagne</li><li>Île-de-France</li></region><settlement><li>Paris</li><li>Rennes</li><li>Toulouse</li></settlement><orgName><li>Université Toulouse III - Paul Sabatier</li><li>Université de Rennes 1</li></orgName></list><tree><country name="France"><region name="Région Bretagne"><name sortKey="Cantat, Serge" sort="Cantat, Serge" uniqKey="Cantat S" first="Serge" last="Cantat">Serge Cantat</name></region><name sortKey="Cantat, Serge" sort="Cantat, Serge" uniqKey="Cantat S" first="Serge" last="Cantat">Serge Cantat</name><name sortKey="Cantat, Serge" sort="Cantat, Serge" uniqKey="Cantat S" first="Serge" last="Cantat">Serge Cantat</name><name sortKey="De Cornulier, Yves" sort="De Cornulier, Yves" uniqKey="De Cornulier Y" first="Yves" last="De Cornulier">Yves De Cornulier</name><name sortKey="De Cornulier, Yves" sort="De Cornulier, Yves" uniqKey="De Cornulier Y" first="Yves" last="De Cornulier">Yves De Cornulier</name><name sortKey="Lamy, Stephane" sort="Lamy, Stephane" uniqKey="Lamy S" first="Stéphane" last="Lamy">Stéphane Lamy</name><name sortKey="Lamy, Stephane" sort="Lamy, Stephane" uniqKey="Lamy S" first="Stéphane" last="Lamy">Stéphane Lamy</name></country><country name="Royaume-Uni"><noRegion><name sortKey="Lamy, Stephane" sort="Lamy, Stephane" uniqKey="Lamy S" first="Stéphane" last="Lamy">Stéphane Lamy</name></noRegion></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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