# ag.algebraic geometry – Hodge construction on intersection cohomology of toric varieties Answer

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ag.algebraic geometry – Hodge construction on intersection cohomology of toric varieties

Given a convex polytope with integer vertices, one can assemble a complicated projective selection $$X$$ known as toric selection. In common $$X$$ will not be flush. As I’ve heard, by the labor of M. Saito, the intersection cohomology of any projective complicated selection, particularly of $$X$$, carries a unaffected absolute Hodge construction.

Is it undoubted that it satisfies
$$H^{p,q}=0 mbox{ if } pne q?$$

This is understood to breathe the illustration if $$X$$ is flush.

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