Let $X\subset A^3_{\mathbb{C}}$ be the affine complex surface defined by $x^r+y^s+z^t=0 $, and let $Y=X-(0,0,0)$. Here $r,s,t\geq2$ are positive integers.
Then what is the fondamental group of $Y$? What can we know from the map $f:Y\to A^2_{\mathbb{C}}-(0,0),\,\,\,x\mapsto x^r,y\mapsto y^s$ ?