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arXiv · 2011.14854

Intersection cohomology and Severi's varieties

Vincenzo Di Gennaro·Davide Franco
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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's 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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Vincenzo Di Gennaro, Davide Franco. 2020-11-30. Intersection cohomology and Severi's varieties. https://arxiv.org/abs/2011.14854

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