2007 Fiscal Year Final Research Report Summary
Combinatorial structures on Riemann surfaces and topological properties of the moduli space
| Project/Area Number |
17540065
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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 | Ochanomizu University |
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Principal Investigator |
KIYOSHI Ohba Ochanomizu University, Graduate School of Humanities and Sciences, associate professor (80242337)
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| Co-Investigator(Kenkyū-buntansha) |
YOKOGAWA Koji Ochanomizu University, Graduate School of Humanities and Sciences, professor (40240189)
HASHIMOTO Yoshitake Osaka City University, Graduate School of Science, associate professor (20271182)
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| Project Period (FY) |
2005 – 2007
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| Keywords | Riemann surfaces / Haefliger knot / Einstein metric / localization / Morley's theorem |
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| Research Abstract |
We consider Riemann surfaces with abelian differentials constructed from lightning pairs. A lightning pair is a piecewise linear loop in the complex plane determined by a certain kind of combinatorial data. During the study of this method we obtained the following results:
1. 1. We gave geometrically a definition of unknotting numbers of a Haefliger (6,3)-knot, which means a smoothly embedded 3-dimensional sphere in the 6-dimensional sphere, and determined the unknotting number of each Haefliger (6,3)-knot.
2. We constructed explicitly a new infinite series of Einstein metrics on the S^3-bundles over S^2, which containing infinite numbers of inhomogeneous ones.
3. We investigated the localization theorem of Beilinson and Bernstein for D^^-^<(m)> on the projective spaces and SL_3 in positive character, and we showed that a tilting sheaf is obtained by taking the dual of the image of the structure sheaf by the Frobenius endomorphism.
4. We presented a short proof of Morley's theorem.
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Research Products
(44 results)
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[Presentation] 5次方程式と正20面体2008
Author(s)
橋本義武
Organizer
高校生と社会人のための現代数学入門講座
Place of Presentation
京都大学
Year and Date
2008-01-12
Description
「研究成果報告書概要(和文)」より
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[Book] 現代幾何学の流れ2007
Author(s)
砂田利一
Total Pages
209-218
Publisher
日本評論社
Description
「研究成果報告書概要(和文)」より
