Study of hyergeometric systems with resonant parameters
| Project/Area Number |
21540001
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Hokkaido University |
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Principal Investigator |
SAITO Mutsumi 北海道大学, 大学院・理学研究院, 准教授 (70215565)
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| Co-Investigator(Kenkyū-buntansha) |
JINZENJI Masao 北海道大学, 大学院・理学研究院, 准教授 (20322795)
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| Co-Investigator(Renkei-kenkyūsha) |
OKUYAMA Go 北海道工業大学, 医療工学部, 准教授 (60433421)
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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 |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2009: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| Keywords | 超幾何系 / D-加群 / 微分作用素環 / トーリック多様体 / レゾナント / 半群環 / ワイル閉包 / レゾナントパラメータ / 超機何系 / 既約加群 / 有限生成系 / 超平面配置 |
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| Research Abstract |
We have proved that an A-hypergeometric system is irreducible if and only if its parameter vector is nonresonant, using the theory of the ring of differential operators on an affine toric variety. In the course of the proof, we have determined the irreducible quotients of an A-hypergeometric system.
We have presented a way of computing a finite system of generators of the first syzygy module of an irreducible A-hypergeometric quotient. In particular, if the semigroup generated by A is simplicial and scored, then an explicit system of generators has been given.
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Report
(4 results)
Research Products
(15 results)
