For a variety $V$ of dimension $n$, let $Irr(V)$ denote the minimal degree of a dominant rational map $V\to \mathbb{P}^n$. 


Suppose that a curve $X$ admits a dominant map from a variety $V$ with $Irr(V)=2$. Does it follow that $X$ is hyperelliptic? 



Degree of irrationality and hyperelliptic curves
Yes, because then there is a nonconstant map from projective space to the symmetric square of $C$.


