Cremona Maps of de Jonquières Type. (1st August 2015)

• Record Type: Journal Article
• Authors: Pan, Ivan; Simis, Aron
• Is Part Of: Canadian journal of mathematics. Volume 67:Number 4(2015)
• Page Start: 923
• Page End: 941
• Publication Date: 2015-08-01
• Subjects: 14E05 -- 13D02 -- 13H10 -- 14E07 -- 14M05 -- 14M25; Cremona map -- de Jonquières map -- Cremona group -- minimal free resolution; Mathematics -- Periodicals; Mathematics; Electronic journals; Periodicals; 510
• DOI: 10.4153/CJM-2014-037-3
• Languages: English
• ISSNs: 0008-414X

Abstract

Abstract: 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.