Intersection cohomology and Severi's varieties

2020/11/30 by Vincenzo Di Gennaro, Di Gennaro, Vincenzo, Davide Franco +1
Mathematics · #14F05 #14F43 #14F45 #14M15 #32S20 #32S60 #58K15 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 14B05 #Secondary 14E15

paper · pdf · doi:10.48550/arxiv.2011.14854

openalex publication_date 2020/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X²ⁿ⊆ ℙ ^N be a smooth projective variety. Consider the intersection cohomology complex of the local system R^2n-1π_*ℚ, where π denotes the projection from the universal hyperplane family of X²ⁿ to (ℙ ^N)^\vee. We investigate the cohomology of the intersection cohomology complex IC(R^2n-1π_*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 ℙ ^N.

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