Exceptional loci in Lefschetz theory

2021/06/18 by Raskin, Sam, Smith, Geoffrey
#14F20 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2106.10332

Abstract

Let ϕ:X→ ℙⁿ be a morphism of varieties. Given a hyperplane H in ℙⁿ, there is a Gysin map from the compactly supported cohomology of ϕ^-1(H) to that of X. We give conditions on the degree of the cohomology under which this map is an isomorphism for all but a low-dimensional set of hyperplanes, generalizing results due to Skorobogatov, Benoist, and Poonen-Slavov. Our argument is based on Beilinson's theory of singular supports for étale sheaves.

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