where can I find the computation of the groups $H^i(\mathbb{P}^n,\Omega_{\mathbb{P}^n}^j)$? Moreover, if $D$ is a divisor with normal crossing in $\mathbb{P}^n$, how can I compute the hypercohomology $$ \mathbb{H}^i(\mathbb{P}^n,\Omega_{\mathbb{P}^n}^j(D)) $$ the case $D=H+I$, with $H,I$ hyperplanes could be also interesting to me (I know that the case with one hyperplane should give the cohomology of affine space). Thanks
differential with logarithmic poles
2
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algebraic-geometry
toric-geometry