Toric rings of configurations constructed by a method with symmetries
| Project/Area Number |
24540055
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Kwansei Gakuin University (2014-2016)
Rikkyo University (2012-2013) |
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Principal Investigator |
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| Project Period (FY) |
2012-04-01 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2016)
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| Budget Amount *help |
¥4,940,000 (Direct Cost: ¥3,800,000、Indirect Cost: ¥1,140,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Keywords | グレブナー基底 / 可換環 / トーリックイデアル / マルコフ基底 / 多面体 / コスツル代数 |
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| Outline of Final Research Achievements |
We studied toric rings of configurations constructed by a method with symmetries such as a centrally symmetric configuration, and discussed various algebraic properties of toric rings and ideals. In particular, we introduced the notion of “configurations of harmony” which yields more reflexive polytopes than the notion of centrally symmetric configurations. In addition, we studied toric ideals arising from various combinatorial objects. For example, we showed that the convex polytope arising from the centrally symmetric configuration of any order polytope is a normal reflexive polytope.
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Report
(6 results)
Research Products
(37 results)
