Let $X\rightarrow D^*$ be fiberation of projective manifold, here $D^*$ means a punctured disk. Then it induces a variation of hodge structure, i.e a holomorphic vector bundle $H_{\mathbb C}$ over $D^*$(the fiber is kth DeRham cohomology group of $X_t$ with coefficient $\mathbb C$). If the monodromy transformation is unipotent, we have isomorphism

$$\mathcal O_{D^*}(H_{\mathbb C})\cong \mathcal O_{D^*}\otimes_{\mathbb C} H$$

The above set-up is my understanding of one of the statement from the paper "variation of hodge structure and singularity of period map" by Wilfried Schmid.

Then I'm a little bit confused about the statement. For me, it seems that the above isomorphism implies that $\mathcal O_{D^*}(H_{\mathbb C})$ is a holomorphic trivial vector bundle, since the RHS is trivial. On the other hand, Kodaira's $I_b$ type singular fiber in elliptic surface has unipotent monodromy but not trivial $H^1$ bundle. So what's wrong with my understanding.

Any comments will be helpful.

notthe MHS of $H^1$ of the closed fibre but there is more complicated relation. $\endgroup$