| Budget Amount *help |
¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
We studied on toric type cusp singularities with the method of Groebner basis. In particular, we proved that cusp singularities are constructed over any field as noetherian complete local rings. We can define the leading terms ideal for an ideal of the local ring, and use it for comparing ideals similarly as the case of the polynomial ring.
In order to generalize and construct cusp singularities, we defined quasi-polyhedral sets and studied some fundamental properties and examples with the action of reflection groups.
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