Pan, Ivan On the Cremona transformations of bidegree (3,3). (Sur les transformations de Cremona de bidegré (3,3).) (French) Zbl 0921.14005 Enseign. Math., II. Sér. 43, No. 3-4, 285-297 (1997). Let \(\mathbb{P}^3\) be three-dimensional projective space over an algebraically closed field \(k\) of characteristic zero. In the paper all birational transformations \(T\) of \(\mathbb{P}^3\) of bidegree \((3,3)\) (this means that equally \(T\) and \(T^{-1}\) have degree \(3\)) are classified into three (not disjoint) classes: (1) the class of determinantal transformations (i.e. components of \(T\) are minors of a \(4\times 3\) matrix the entries of which are linear forms on \(k^4\)), (2) the Jonquières class of transformations (i.e. the strict transformation \(\overline{T^{-1}(L)}\) of a generic line \(L\) is a plane cubic), (3) the ruled class of transformations (i.e. the strict transformation \(\overline{T^{-1}(H)}\) of a generic plane \(H\) is a ruled cubic surface). Reviewer: T.Krasiński (Łódź) Cited in 10 Documents MSC: 14E07 Birational automorphisms, Cremona group and generalizations 14E05 Rational and birational maps Keywords:birational mapping; Cremona transformation PDFBibTeX XMLCite \textit{I. Pan}, Enseign. Math. (2) 43, No. 3--4, 285--297 (1997; Zbl 0921.14005)