Consider an algebraic elliptic surface $f :X \rightarrow C$ with $\chi(X) > 0$
or equivalently the fibration has reduced singular fibers (the field under consideration
is $\mathbb{C}$).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?.