| Project/Area Number |
13640067
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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 |
Geometry
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| Research Institution | The University of Electro-Communications |
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Principal Investigator |
YAMAGUCHI Kohei Univ.Electro-Commun., Fac.of Elector-Commun., Professor, 電気通信学部, 教授 (00175655)
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| Co-Investigator(Kenkyū-buntansha) |
OHNO Masahiro Univ.Electro-Commun., Fac.of Elector-Commun., Asso.Prof., 電気通信学部, 助教授 (70277820)
KIDA Masanari Univ.Electro-Commun., Fac.of Elector-Commun., Asso.Prof., 電気通信学部, 助教授 (20272057)
NAITO Toshiki Univ.Electro-Commun., Fac.of Elector-Commun., Professor, 電気通信学部, 教授 (60004446)
ISHIDA Haruhisa Univ.Electro-Commun., Fac.of Elector-Commun., Lecturer, 電気通信学部, 講師 (80312792)
YAMADA Yuichi Univ.Electro-Commun., Fac.of Elector-Commun., Lecturer, 電気通信学部, 講師 (30303019)
安藤 清 電気通信大学, 電気通信学部, 教授 (20096944)
田吉 隆夫 電気通信大学, 電気通信学部, 教授 (60017382)
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| Project Period (FY) |
2001 – 2003
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| Project Status |
Completed (Fiscal Year 2003)
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| Budget Amount *help |
¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2003: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2002: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 2001: ¥1,500,000 (Direct Cost: ¥1,500,000)
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| Keywords | projective variety / Riemann surface / energy functional / configuration space / harmonic map / elliptic curve / algebraic torus / asymptic stability / リーマン画 / ラベル付き粒子の配置空間 / ラグラジアン / ホモトピー型 / 正則写像 / 曲面結び目 / labelled configuration space / 射影空間 / モース理論的原理 / universal covering / だ円曲線 / 高次分岐群 |
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| Research Abstract |
Consider the energy functionals E on spaces consisting of all smooth maps from a Riemann surface to complex projective spaces. In this case, it is very important to study the spaces consisting of all critical points of E.K.Yamaguchi suceeds to define a finite dimensional homotopy configuration space models from a Riemann surface of genus g into a complex projective space for g>O. He also obtains a similar result for the space of algebraic maps between real projective spaces. Moreover, he shows that a homotopy asymptic stability theorem holds for such spaces of algebraic maps. Kida studies elliptic curves and algebraic field extensions associated to certain maps on algebraic torus. As an application he obtains an easy method for checking prime numbers. M.Ohno studied the vector bundles over non-singular projective varieties and investigated them from the point of view of "nef value". Y.Yamada studied the topology of 4-manifolds and obtained several results related to Gluck surgery.
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