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.
CITATION STYLE
Foth, P. A. (1999). Logarithmic Forms with Twisted Coefficients. In Advances in Geometry (pp. 183–193). Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-1770-1_9
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