Let $f(x,y) \in C[x,y]$ be a quasi-homogeneous polynomial, with
$f(t^{w_1}x,t^{w_1}y)=t^df(x,y)$
Supposedly, after an analytic change of variables, we can always write it as:
$f(x,y) = \underset{i=1}{\overset{d}{\prod}}(y^p-a_{i}x^q)^{c_i}$,
where $(p,q)=1$.
Why is this?
Thank you!