Logarithmic forms with twisted coefficients
Differential Geometry
2007-05-23 v1 Algebraic Geometry
Abstract
Given a compact Kaehler manifold, we consider the complement U of a divisor with normal crossings and a unitary local system V on it. We consider a differential graded Lie algebra (DGLA) of forms with holomorphic logarithmic singularities and vanishing residues. We construct a spectral sequence corresponding to the anti-holomorphic filtration of this algebra and compute its E1 term. This spectral sequence converges to the L2 cohomology H2*(U, V). We show that this DGLA is formal, although it does not always satisfy to the d'd''-Lemma.
Cite
@article{arxiv.math/9802005,
title = {Logarithmic forms with twisted coefficients},
author = {Philip Foth},
journal= {arXiv preprint arXiv:math/9802005},
year = {2007}
}
Comments
12 pages LaTeX