Abstract
Let $$X^{2n}\subseteq \mathbb {P}^N$$ be a smooth projective variety. Consider the intersection cohomology complex of the local system $$R^{2n-1}\pi {_*}\mathbb {Q}$$ , where $$\pi $$ denotes the projection from the universal hyperplane family of $$X^{2n}$$ to $${(\mathbb {P}^N)}^{\vee }$$ . We investigate the cohomology of the intersection cohomology complex $$IC(R^{2n-1}\pi {_*}\mathbb {Q})$$ over the points of a Severi variety, parametrizing nodal hypersurfaces, whose nodes impose independent conditions on the very ample linear system giving the embedding in $$\mathbb {P}^N$$ .
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