2023
DOI: 10.1093/imrn/rnad019
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Mixed Hodge Structure on Local Cohomology with Support in Determinantal Varieties

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.

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