A study on mixed Hodge structures on the relative log de Rham cohomology groups of log smooth degenerations

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In 2006, I studied the case of semi-stable degeneration of compact Kahler complex manifolds, as an important example of log smooth degenerations. In particular, weight filtrations on the mixed Hodge complexes constructed on the singular fibers were considered deeply. I found that the properties of these weight filtrations were related to the properties of monodromy logarithmsIn 2007, I have been studying these weight filtrations and found that the monodromy logarithms played important roles to construct the weight filtrations for the case of log smooth degenerations.The monodromy action on the cohomology groups is quasi-unipotent in general. However I expect that we can construct mixed Hodge complexes, for the case of log smooth degeneration, by the reduction to the case where the monodromy actions are unipotent, once I find out the appropriate conditions which assures the unipotency of the monodromy.In order to find out such conditions, I calculated the cohomology sheaves of the relative log de Rham complexes for log smooth degenerations.