Cremona Maps of de Jonquières Type. (1st August 2015) - Pan, Ivan
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.