Let $K=\mathbb{C}(t_1,\dots,t_n)$ be the field of rational functions, $f$ an algebraic function over $K$ and assume the field extension $K(f)/K$ is non-solvable. Is it possible to characterise the indeterminacy locus of $f$?
The proof of Step 3 in Theorem 3.10 in Sendra, Sevilla & Villarino (2017) shows that, in the case of solvable extensions, the indeterminacy locus is contained in a lower dimensional variety, but I'd like to understand what happens in general. My background in algebraic geometry is at the level of Cox, Little, O'Shea "Ideas, Varieties and Algorithms".
