| Project/Area Number |
12640022
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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 | International Christian University |
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Principal Investigator |
SHIMIZU Yuji International Christian University (ICU), College of Liberal Arts, Associate Professor, 教養学部, 準教授 (80187468)
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| Co-Investigator(Kenkyū-buntansha) |
YAMAKAWA Aiko ICUJ Assistant Professor College of Liberal Arts, 教養学部, 助教授 (80112754)
SUZUKI Hiroshi ICU Professor College of Liberal Arts, 教養学部, 教授 (10135767)
MORIMOTO Mitsuo ICU Professor College of Liberal Arts, 教養学部, 教授 (80053677)
SAITO Masa-hiko Kobe Univ. Professor Faculty of Science, 理学部, 教授 (80183044)
UENO Kenji Kyoto Univ. Professor Graduate School of Science, 大学院・理学研究科, 教授 (40011655)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 2002: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥1,400,000 (Direct Cost: ¥1,400,000)
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| Keywords | raional elliptic surfaces / Seiberg-Witten theory / period map / integrable system / conformal field theory / elliptic K3 surfaces / drived category |
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| Research Abstract |
On the theme of Seiberg-Witten theory approached through elliptic surfaces, Shimizu did the joint research with A.Tsuchiya (Nagoya Univ.), A.Kato (Unlv. Tokyo) Y.Saito (Univ. Tokyo), H.Awata (Univ. Tokyo) etc. Among others, we constructed the moduli space of marked rational elliptic surfaces and their period map, studied the inversion problem, the relation with simply elliptic singularities, constructed the elliptic Lie algebra and the elliptic Weyl group, and carried out the realization of a Seiberg-Witten integrable system. In 2002, we introduced the periods of elliptic K3 surfaces, the moduli and the derived category of coherent sheaves in order to enlarge our study and to look for the quantum analog of classical periods
Ueno and Shimizu studied the degeneration behavior of the conformal blocks of the CFT with abelian currents as symmetries, and published a book on moduli theory. Ueno constructed a modular functor using CFT. From the viewpoint of deformation theory of complex structure, Saito reconsidered the space of initial values of the Painleve equations, introduced the notion of Okamoto-Painleve pairs, classified them and rewrited the differential equations
Suzuki studied weakly distance-regular digraphs and type II matrices associated with link invariants. Morimoto expressed the analytic functionals on the sphere as initial values of the heat functions. Yamakawa studied codimension one locally free action of solvable Lie groups
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