Construction of theory of geometric and combinatorial deformations of toric rings
| Project/Area Number |
21740030
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Rikkyo University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | 環論 / グレブナー基底 / トーリックイデアル / トーリック環 / 多面体 |
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| Research Abstract |
We study geometric and combinatorial deformations of toric rings and show that a lot of properties of toric rings are inherited by taking a nested configuration that is a generalization of the basic operations, such as the product of polytopes. Moreover, for integer matrices, we define centrally symmetric configurations and prove that their toric rings has good properties (normal and Gorenstein etc.). In addition, it is shown that the normality of cut polytopes is closed under taking a minor and a clique sum.
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Report
(4 results)
Research Products
(32 results)
