| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
This research program aims at studying the freeness of hyperplane arrangemens more deeply, and investigate its geometry. These aims are achieved and the results are better than we expected. First, for any ideal subarrangements of Weyl arrangements coming from an ideal which is certain subsets of positive roots, we determine its Betti numbers by using freeness which coincides with the dual partition of height distributions of roots in the ideal. Next, we improved Terao's addition-deletion theorem invented in 1980 into the division theorem for free arrangements. By applying it, we enlarged the class in which the freeness depends only on combinatorics, and named divisionally free arrangements. These two results are of the great advances in this research area, so we think this research program is achieved successfully.
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