Smooth projective hypersurface has zero irregularity
= Smooth projective hypersurface has zero irregularity
A smooth surface hypersurface $X_d\subseteq\mathbb P^3$ has $q(X_d)=0$. This follows from the <structure-sheaf sequence of a hypersurface> and the vanishing of the intermediate cohomology of line bundles on $\mathbb P^3$.