Some remarks on decomposition theorem for proper Kähler morphisms

2022/04/19 by Saito, Morihiko
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.09026

Abstract

We explain a correct proof of the decomposition theorem for direct images of constant Hodge modules by proper Kähler morphisms of complex manifolds. We also give some examples showing certain difficulty in the non-constant Hodge module case.

Related

• Hodge modules and Kähler morphisms
• Hodge-theoretic aspects of the Decomposition Theorem
• Hodge decomposition theorem on compact d-Kähler manifolds
• The Hodge theory of the Decomposition Theorem (after de Cataldo and Migliorini)
• Hodge modules on complex tori and generic vanishing for compact Kähler manifolds