Logarithmic form: Difference between revisions

Revision as of 17:21, 18 August 2011

Revision as of 19:01, 20 August 2011

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:<math> \Omega^{\bullet}_Y(\log D)\rightarrow j_*\Omega_{X}^{\bullet} </math>

turns out to be a quasi-isomorphism. Thus

:<math> H^k(X;\mathbb{C}) = \mathbb{H}^k(Y, \Omega^{\bullet}_X_Y(\log D))</math>

where <math> \mathbb{H}^{\bullet} </math> denotes [[hypercohomology]] of a complex of abelian sheaves. There is<ref name="foo"/> a decreasing filtration <math> W_{\bullet}\Omega^p_X(\log D) </math> given by

:<math>W_{m}\Omega^p_X(\log D) = \begin{cases}