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Cremona Maps of de Jonquières Type

Published online by Cambridge University Press:  20 November 2018

Ivan Pan  and
Aron Simis
Ivan Pan
Affiliation:
Centro de Matemática, Facultad de Ciencias, Universidad de la República, 11400 Montevideo, UruguayDepartamento de Matemática, CCEN, Universidade Federal de Pernambuco, 50740-560 Recife, PE, Brazil e-mail: ivan@cmat.edu.uy
Aron Simis
Affiliation:
Departamento de Matemática, CCEN, Universidade Federal da Paraíba, 58059-900 João Pessoa, PB, Brazil e-mail: aron@dmat.ufpe.br
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Abstract

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This paper is concerned with suitable generalizations of a plane de Jonquières map to higher dimensional space ${{\mathbb{P}}^{n}}$ with $n\,\ge \,3$. For each given point of ${{\mathbb{P}}^{n}}$ there is a subgroup of the entire Cremona group of dimension $n$ consisting of such maps. We study both geometric and group-theoretical properties of this notion. In the case where $n\,=\,3$ we describe an explicit set of generators of the group and give a homological characterization of a basic subgroup thereof.

Keywords

14E0513D0213H1014E0714M0514M25Cremona mapde Jonquières mapCremona groupminimal free resolution
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 4 , 01 August 2015 , pp. 923 - 941
Copyright
Copyright © Canadian Mathematical Society 2015

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