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# Cremona Maps of de Jonquières Type

Published:2014-11-26
Printed: Aug 2015
• Ivan Edgardo Pan,
Centro de Matemática, Facultad de Ciencias, Universidad de la República, 11400 Montevideo, Uruguay
• Aron Simis,
Departamento de Matemática, CCEN, Universidade Federal de Pernambuco,
 Format: LaTeX MathJax PDF

## Abstract

This paper is concerned with suitable generalizations of a plane de Jonquières map to higher dimensional space $\mathbb{P}^n$ with $n\geq 3$. For each given point of $\mathbb{P}^n$ there is a subgroup of the entire Cremona group of dimension $n$ consisting of such maps. One studies both geometric and group-theoretical properties of this notion. In the case where $n=3$ one describes an explicit set of generators of the group and gives a homological characterization of a basic subgroup thereof.
 Keywords: Cremona map, de Jonquières map, Cremona group, minimal free resolution
 MSC Classifications: 14E05 - Rational and birational maps 13D02 - Syzygies, resolutions, complexes 13H10 - Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05] 14E07 - Birational automorphisms, Cremona group and generalizations 14M05 - Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10] 14M25 - Toric varieties, Newton polyhedra [See also 52B20]

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