Consider an elliptic surface $f :X \rightarrow C$ with $\chi(X) > 0$ or equivalently the fibration has reduced singular fibers (the field under consideration is $\mathbb{C}$,$X$,$C$ are smooth and projective ). Denote by $\Omega$ the cotangent bundle of $X$ and $K$ the canonical bundle of $C$. We have an inclusion \begin{equation} 0 \rightarrow f^*K \rightarrow \Omega \end{equation} Let $q(X)$ denote the dimension of $H^0(X,\Omega)$ over $\mathbb{C}$. We have $q(X) = g$ where $g$ is the genus of the curve $C$.On the other hand dimension of $H^{0}(C,K)$ is $g$ as well and hence we get (using the above inclusion of sheaves) \begin{equation} H^{0}(C,K) = H^{0}(X,\Omega). \end{equation} Now what I am trying to understand is the above equality in a better way (rather than just by using the dimension argument as above). Is there a way to see why all the 1-forms are pull backs of those from the base curve?.