Mixed Hodge structures associated to geometric variations
Donu Arapura
TL;DR
This paper proves that the mixed Hodge structure for geometric variations aligns with Saito's mixed Hodge module theory, clarifying the relationship between these two approaches in Hodge theory.
Contribution
It establishes the equivalence of two constructions of mixed Hodge structures for geometric variations, connecting previous work with Saito's theory.
Findings
The mixed Hodge structure from the author's earlier construction coincides with Saito's structure.
The paper clarifies the relationship between different approaches to mixed Hodge structures.
Includes an erratum for the previous publication.
Abstract
The purpose of this note is prove that the mixed Hodge structure constructed by the author in math.AG/0301140 [The Leray spectral sequence is motivic, Invent. 2005] for geometric variations of Hodge structure coincides with the structure coming from M. Saito's mixed Hodge module theory. This note also contains a small erratum for the earlier paper.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology