2003 Fiscal Year Final Research Report Summary
Topology related to Valuation problems and Numerical Computations
| 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)
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| Project Period (FY) |
2001 – 2003
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| Keywords | projective variety / Riemann surface / energy functional / configuration space / harmonic map / elliptic curve / algebraic torus / asymptic stability |
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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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