2009 Fiscal Year Final Research Report
Applications of algebraic analysis to geometry
| Project/Area Number |
19540163
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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 |
Basic analysis
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| Research Institution | University of Tsukuba |
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Principal Investigator |
TAKEUCHI Kiyoshi University of Tsukuba, 大学院・数理物質科学研究科, 准教授 (70281160)
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| Co-Investigator(Kenkyū-buntansha) |
SUWA Tatsuo 北海道大学, 名誉教授 (40109418)
TAJIMA Shinichi 筑波大学, 大学院・数理物質科学研究科, 教授 (70155076)
TANISAKI Toshiyuki 大阪市立大学, 大学院・理学研究科, 教授 (70142916)
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| Project Period (FY) |
2007 – 2009
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| Keywords | D加群 / 超幾何関数 / 特異点理論 / テドン変換 / 偏屈層 / モノドロミー |
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| Research Abstract |
We studied Lefschetz fixed point formulas for maps with higher-dimensional fixed point sets and obtained a formula which expresses their fixed point indices explicitly. We also obtained formulas describing the dimensions and the degrees of A-discriminant varieties introduced by Gelfand etc. in terms of the geometric data of the configuration A.Moreover, as byproducts of this research, various results on the monodromies at infinity of polynomial maps, the analytic continuations of A-hypergeometric functions and the poles of local zeta functions etc. are also obtained.
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