| Outline of Final Research Achievements |
In this research, we studied the Solomon-Terao polynomial theory, which attracts many interests recently, from the viewpoint of the D-modules, in particular, that of so called the Liouville complex theory due to Uli Walther. On this approach, a joint work with Castro and Narvaez in Sevilla, we observed that the freenss of arrangements coincides with the Cohen-Macaulayness of the Liouville algebra, and a specializaion of the Liouville complex coincides with the Solomon-Terao complex. This shows that in a very high possibility, the Liouville complex theory could be regarded as a two-variable version of the Solomon-Terao complex theory. This enlarges the research of this area drastically. Also, in a joint work with Graham Denahm in Western university, we proved the Ziegler's conjecture on the logarithnmic differential forms. This was conjectured about 30 years before, and we investigated a theory to show it.
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