2016 Fiscal Year Final Research Report
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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| Keywords | グレブナー基底 / 可換環 |
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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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| Free Research Field |
計算可換代数
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