Hodge filtration on local cohomology, Du Bois complex and local cohomological dimension

We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions and derive applications regarding the local cohomological dimension, the Du Bois complex, local vanishing and reflexive differentials associated...

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Bibliographic Details
Published in:Forum of mathematics. Pi 2022-01, Vol.10, Article e22
Main Authors: Mustaţă, Mircea, Popa, Mihnea
Format: Article
Language:English
Subjects:
14B05
14B15
14F10
14F17
32S35
Algebraic and Complex Geometry
Filtration
Homology
Sheaves
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Summary:We study the Hodge filtration on the local cohomology sheaves of a smooth complex algebraic variety along a closed subscheme Z in terms of log resolutions and derive applications regarding the local cohomological dimension, the Du Bois complex, local vanishing and reflexive differentials associated to Z.
ISSN:2050-5086
2050-5086
DOI:10.1017/fmp.2022.15