On Cremona transformations of \(\mathbb{P}^3\) with all possible bidegrees
A Cremona map \(F:\mathbb P^3\dashrightarrow\mathbb P^3\) has bidegree \((d,e)\) if \(F\) is defined by homogeneous polynomials of degree \(d\) and \(F^{-1}\) by homogeneous polynomials of degree \(e\). The author proves the existence of such maps for all bidegrees \((d,e)\) with \(d, e\geq 2\) and \(\sqrt{d}\leq e\leq d^2\). This corrects a mistake in [C. R. Acad. Sci., Paris, Sér. I, Math. 330, No. 4, 297--300 (2000; Zbl 1011.14003)]. Explicit constructions are given.
scientific article; zbMATH DE number 6211815