Relative log Poincar e lemma and relative log de Rham theory

Abstract

In this paper we will generalize the classical relative Poincar e lemma in the framework of log geometry. Like the classical Poincar e lemma directly implies the de Rham theorem, the comparison between de Rham and Betti cohomologies, our log Poincar e lemma yields the formula which gives integral structures of hyperdirect images of the log de Rham complexes; these integral structures are nothing but the integral structures of degenerate VMHS in the semistable degeneration case. We will also develop the relative log de Rham theory for semistable degeneration and recover the well-known result of Steenbrink.

Cite this paper

@inproceedings{Kato1998RelativeLP, title={Relative log Poincar e lemma and relative log de Rham theory}, author={Fumiharu Kato}, year={1998} }