Suppose $P$ is a variety over $\mathbb{C}$(in my case $P$ might have slight singularities), and $V=\cap_{i}^{r} D_i$ is a complete intersection. Then, it is claimed exists the so called "Standard exact sequence for a complete intersection":

$$0 \to O_{V}(-D_1) \oplus \cdots \oplus O_{V}(-D_r) \to \Omega_{P}^{1}|\_V \to \Omega_{V}^1 \to 0.$$

Does anyone know how to show the above exact sequence? Or point out some reference having discussiong about such things? Moreover, what are the corresponding sequence for the $p$-forms (i.e. the sequence tells something about $\Omega\_{P}^{p}|_V $ and $\Omega\_{V}^p $ )?