Noninvolutorial Cremona transformations in [𝑛

Abstract

There are, in the literature, many examples of noninvolutorial Cremona transformations in the plane, in ordinary space, and in higher space of definite dimension. But comparatively few such transformations are known for space of n dimensions, where the n is general. This paper presents an extensive series of noninvolutorial Cremona transformations between two n-dimensional projective spaces (n any positive integer), developed by a new method, and classifies them. Very many known transformations may be obtained by assigning particular values to our general coefficients and by composition.