Quotients of groups of birational transformations of cubic del Pezzo fibrations
| Autor: | Jérémy Blanc, Egor Yasinsky |
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| Rok vydání: | 2020 |
| Předmět: |
Normal subgroup
Pure mathematics 14E07 14E05 14E30 14J45 14M22 Group (mathematics) General Mathematics Fibration Mathematics - Algebraic Geometry Mathematics::Group Theory Mathematics::Algebraic Geometry Cremona group Free product Simple (abstract algebra) Order (group theory) Group homomorphism Mathematics - Group Theory Mathematics |
| Zdroj: | Journal de l’École polytechnique — Mathématiques. 7:1089-1112 |
| ISSN: | 2270-518X |
| DOI: | 10.5802/jep.136 |
| Popis: | We prove that the group of birational transformations of a Del Pezzo fibration of degree 3 over a curve is not simple, by giving a surjective group homomorphism to a free product of infinitely many groups of order 2. As a consequence we also obtain that the Cremona group of rank 3 is not generated by birational maps preserving a rational fibration. Besides, its subgroup generated by all connected algebraic subgroups is a proper normal subgroup. Comment: to appear in JEP |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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