= Polynomial multiplication map to complex projective space
{title2=$(\mathbb{CP}^1)^m\to\mathbb{CP}^m,\quad (L_1,\ldots,L_m)\mapsto\prod_iL_i$}
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>.
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