2021/03/06 by Junchao Shentu, Chen Zhao, Shentu, Junchao +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds
paper · pdf · doi:10.48550/arxiv.2103.04030
openalex publication_date 2021/03/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Over an arbitrary compact complex space or an arbitrary germ of complex space X, we provide fine resolutions of pure Hodge modules with strict supports ICX(\mathbbV) via differential forms with locally L2 boundary conditions. When \mathbbV=ℂ_X\rm reg is the trivial variation of Hodge structure, we give a solution to a Cheeger-Goresky-MacPherson type conjecture: For any compact complex space X, there is a complete hermitian metric ds2 on X\rm reg such that there is a canonical isomorphism Hi(2)(X\rm reg,ds2)≃ IHi(X), ∀ i. Such metric ds2 could be Kähler if X is a Kähler space. As an application, we give a differential geometrical proof of the Kähler package of the hypercohomology of pure Hodge modules. We also prove the Kähler version of Kashiwara's conjecture in the absolute case.