The discriminant embedding

Abstract

We construct a map from the complex projective n-space into a (3(n+1)n/2-1)-dimensional sphere, called discriminant embedding. In case n = 1, the discriminant embedding is the Riemann sphere map. To show that the discriminant embedding is in fact an immersion, we calculate the determinant of a matrix resulting from its Jacobian. This is related to constructions of G. Mannoury and B. A. Fuks.