 Polynomial multiplication map to complex projective space

Identify ${\mathbb{CP}}^m$ with nonzero homogeneous binary forms of degree $m$, modulo nonzero scalar multiplication. Multiplication of $m$ projective linear forms gives a well-defined holomorphic map: no product is zero, and scaling one form scales the entire coefficient vector. A form with $m$ distinct roots has exactly $m!$ ordered factorizations. In affine root coordinates the derivative is a Vandermonde determinant, nonzero at distinct roots. Each such preimage contributes $+1$ with complex orientations, so the mapping degree is $m!$. This also realizes the least positive degree allowed by the factorial degree obstruction for products of two-spheres.