Urech, Christian.
(2016)
* On homomorphisms between Cremona groups.*
Preprints Fachbereich Mathematik, 2016 (04).

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## Abstract

We look at algebraic embeddings of the Cremona group in n variables $Cr_n(\mathbb{C})$ to the groups of birational transformations Bir(M) of an algebraic variety M. First we study geometrical properties of an example of an embedding of $Cr_2(\mathbb{C})$ into $Cr_5(\mathbb{C})$ that is due to Gizatullin. In a second part, we give a full classification of all algebraic embeddings of $Cr_2(\mathbb{C})$ into Bir(M), where dim(M) = 3 and generalize this result partially to algebraic embeddings of $Cr_n(\mathbb{C})$ into Bir(M), where dim(M) = n + 1, for arbitrary n. In particular, this yields a classification of all algebraic $PGL_{n+1}(\mathbb{C})$-actions on smooth projective varieties of dimension n + 1 that can be extended to rational actions of $Cr_n(\mathbb{C})$.

Faculties and Departments: | 05 Faculty of Science > Departement Mathematik und Informatik > Mathematik > Algebra (Blanc) 12 Special Collections > Preprints Fachbereich Mathematik |
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UniBasel Contributors: | Urech, Christian |

Item Type: | Preprint |

Publisher: | Universität Basel |

Language: | English |

Last Modified: | 06 May 2019 22:52 |

Deposited On: | 28 Mar 2019 09:51 |

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