Deligne-Hodge-DeRham theory with coefficients

Details Deligne-Hodge-DeRham theory with coefficients Deligne-Hodge-DeRham theory with coefficients

2007-02-04

arxiv.org/abs/math/0702083v1

Mathematics

Algebraic Geometry

33 pages

Scientific paper

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 $\Psi_f ({\cal L})$ 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.

Affiliated with

Also associated with

No associations

Rating

Deligne-Hodge-DeRham theory with coefficients does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Deligne-Hodge-DeRham theory with coefficients, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Deligne-Hodge-DeRham theory with coefficients will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-496700