Document Type
Article
Publication Date
1-1-2025
Abstract
Let H = ((H, F •), L) be a polarized variation of Hodge structure on a smooth quasi-projective variety U . By M. Saito’s theory of mixed Hodge modules, the variation of Hodge structure H can be viewed as a polarized Hodge module M ∈ HM (U ). Let X be a compactification of U , and j : U ↪→ X is the natural map. In this paper, we use local cohomology with mixed Hodge module theory to study j+M ∈ DbM HM (X). In particular, we study the graded pieces of the de Rham complex GrF p DR(j+M) ∈ Db coh(X), and the Hodge structure of Hi(U, L) for i in sufficiently low degrees
Recommended Citation
Hiatt, S. (2025). Vanishing of local cohomology with applications to Hodge theory. In Journal of Algebra (Vol. 661, pp. 160–192). Elsevier BV. https://doi.org/10.1016/j.jalgebra.2024.07.036
Comments
A preprint is available to download from this page, the official published research paper available from the DOI.