2011 Fiscal Year Final Research Report
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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| 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 |
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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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