Mixed Hodge structure on local cohomology with support in determinantal varieties
Algebraic Geometry
2023-01-23 v2 Commutative Algebra
Abstract
We employ the inductive structure of determinantal varieties to calculate the mixed Hodge module structure of local cohomology modules with determinantal support. We show that the weight of a simple composition factor is uniquely determined by its support and cohomological degree. As a consequence, we obtain the equivariant structure of the Hodge filtration on each local cohomology module. Finally, as an application, we provide a formula for the generation level of the Hodge filtration on these modules.
Keywords
Cite
@article{arxiv.2102.04369,
title = {Mixed Hodge structure on local cohomology with support in determinantal varieties},
author = {Michael Perlman},
journal= {arXiv preprint arXiv:2102.04369},
year = {2023}
}
Comments
17 pages, v2: Strengthened main theorem (Theorem 3.1) to include indecomposable summands of local cohomology. Corrected errors in Section 2 and Section 3. To appear in IMRN