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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,
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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 Cremona map, de Jonquières map, Cremona group, minimal free resolution
MSC Classifications: 14E05, 13D02, 13H10, 14E07, 14M05, 14M25 show english descriptions Rational and birational maps
Syzygies, resolutions, complexes
Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.) [See also 14M05]
Birational automorphisms, Cremona group and generalizations
Varieties defined by ring conditions (factorial, Cohen-Macaulay, seminormal) [See also 13F15, 13F45, 13H10]
Toric varieties, Newton polyhedra [See also 52B20]
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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