Deligne-Hodge-DeRham theory with coefficients
| dc.creator | Elzein, Fouad | |
| dc.date | 2007-02-04 | |
| dc.date.accessioned | 2026-07-07T07:44:47Z | |
| dc.date.available | 2026-07-07T07:44:47Z | |
| dc.description | Let ${\cal L}$ 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.description | 33 pages | |
| dc.identifier | https://arxiv.org/abs/math/0702083 | |
| dc.identifier | http://arxiv.org/abs/math/0702083 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/123326 | |
| dc.subject | Algebraic Geometry | |
| dc.subject | 32S35 (primary), 32G20, 14D07 (secondary) | |
| dc.title | Deligne-Hodge-DeRham theory with coefficients | |
| dc.type | text |