Deligne-Hodge-DeRham theory with coefficients

dc.creatorElzein, Fouad
dc.date2007-02-04
dc.date.accessioned2026-07-07T07:44:47Z
dc.date.available2026-07-07T07:44:47Z
dc.descriptionLet ${\cal L}$ be a variation of Hodge structures on the complement $X^{*}$ of a normal crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and let $ j: X^{*} = X - Y \to X $ denotes the open embedding. The purpose of this paper is to describe the weight filtration $W$ on a combinatorial logarithmic complex computing the (higher) direct image ${\bf j}_{*}{\cal L} $, underlying a mixed Hodge complex when $X$ is proper, proving in this way the results in the note [14] generalizing the constant coefficients case. When a morphism $f: X \to D$ to a complex disc is given with $Y = f^{-1}(0)$, the weight filtration on the complex of nearby cocycles $Ψ_f ({\cal L})$ on $Y$ can be described by these logarithmic techniques and a comparison theorem shows that the filtration coincides with the weight defined by the logarithm of the monodromy which provides the link with various results on the subject.
dc.description33 pages
dc.identifierhttps://arxiv.org/abs/math/0702083
dc.identifierhttp://arxiv.org/abs/math/0702083
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123326
dc.subjectAlgebraic Geometry
dc.subject32S35 (primary), 32G20, 14D07 (secondary)
dc.titleDeligne-Hodge-DeRham theory with coefficients
dc.typetext

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