| Project/Area Number |
15340018
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Sophia University |
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Principal Investigator |
TSUJI Hajime Sophia University, Department of Mathematics, Professor, 理工学部, 教授 (30172000)
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| Co-Investigator(Kenkyū-buntansha) |
FUTAKI Akito Tokyo Institute of Technology, Department of Mathematics, Professor, 理工学部, 教授 (90143247)
ISHII Shihoko Tokyo Institute of Technology, Department of Mathemtaics, Professor, 理工学部, 教授 (60202933)
藤田 隆夫 東京工業大学, 理工学部, 教授 (40092324)
加藤 昌英 上智大学, 理工学部, 教授 (90062679)
篠田 健一 (筱田 健一) 上智大学, 理工学部, 教授 (20053712)
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| Project Period (FY) |
2003 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥8,100,000 (Direct Cost: ¥8,100,000)
Fiscal Year 2006: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2005: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2004: ¥2,000,000 (Direct Cost: ¥2,000,000)
Fiscal Year 2003: ¥2,100,000 (Direct Cost: ¥2,100,000)
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| Keywords | pluricanonical systems / varieties of general type / Kaehler-Einstein metrics / closed positive current / singular hermitian metrics / analytic Zariski decomposition / Bergman kernel / plurisubharmonicity / ベルグマン核 / 多重標準系 / タイヒミュラー空間 / ベクトル束 / 変形 / ケーラー多様体 / ケーラーアインシュタイン計量 / 一般型代数多様体 / モジュライ空間 / 乗数イデアル層 / 剛性定理 / モジュライ / 代数多様体 / 双有理幾何学 |
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| Research Abstract |
I obtain that there exists a positive number m(n) dependeing only on n such that for every smooth projective n-fold of general type and for every positive integer m> m(n), mK_{X} gives a birtaional embedding of X into a projective space.
This is a furthere generalization of the result of E. Bombieri for surfaces of general type.
Next I proved that the for a smooth projective family f X longrightarrow S and a semipositive singular hermitian line bundle L,
The adjoint bundle K {X/S} + L has a Bergman kernel which is logarithmically plurisubharmonic on $X$.
Moreover the curvature current extends to the whole completion as a closed positive current.
3rd I have proven a new construction of Kaehler-Einstein metric with negative Ricci curvature. This enables us to study the variation of Kaehler-Einstein volume form on a smooth projective family of canonically polarized varieties.
As a consequence I have obtained the plurisubharmonic variation of the Kaehler-Einstein volume form on a smooth projective Family.
4^<th>. I have constructed a canonical singular hermitian metric on the canonical bundle of any nonuniruled projective varieties with semipositive curvature current. And minimal singularities (AZD).
This enables us to obtain a very short proof of the invariance of plurigenera.
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