| Project/Area Number |
16204006
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | Osaka University |
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Principal Investigator |
MABUCHI Toshiki Osaka University, Graduate School of Science, Professor (80116102)
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| Co-Investigator(Kenkyū-buntansha) |
NAKAJIMA Hiraku Kyoto University, Graduate Schcol of Science, Professor (00201666)
ONO Kaoru Hokkaido University, Graduate School of Science, Professor (20204232)
ITOH Mitsuhiro University of Thukuba, Graduate Schcol of Pure and Applied Sciences, Professor (40015912)
UMEHARA Masaaki Osaka University, Graduate Schcol of Science, Professor (90193945)
GOTO Ryushi Osaka University, Graduate School of Science, Associate Professor (30252571)
作間 誠 大阪大学, 大学院理学研究科, 助教授 (30178602)
小松 玄 大阪大学, 大学院理学研究科, 助教授 (60108446)
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| Project Period (FY) |
2004 – 2007
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| Project Status |
Completed (Fiscal Year 2007)
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| Budget Amount *help |
¥27,820,000 (Direct Cost: ¥21,400,000、Indirect Cost: ¥6,420,000)
Fiscal Year 2007: ¥7,280,000 (Direct Cost: ¥5,600,000、Indirect Cost: ¥1,680,000)
Fiscal Year 2006: ¥6,890,000 (Direct Cost: ¥5,300,000、Indirect Cost: ¥1,590,000)
Fiscal Year 2005: ¥6,370,000 (Direct Cost: ¥4,900,000、Indirect Cost: ¥1,470,000)
Fiscal Year 2004: ¥7,280,000 (Direct Cost: ¥5,600,000、Indirect Cost: ¥1,680,000)
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| Keywords | geometry / extremal metric / stability / balanced metric / degeneration / constant scalar curvature / test configuration / obstruction / Test configuration / Hitchin-Kobayashi対応 / 定スカラー曲率ケーラー計量 / 漸近安定性 / Chow-mumford安定性 / Hilbert-mumford安定性 / extremal-Kahler計算 / 偏極代数多様体 / 存在問題 / Chow-Mumford漸近安定性 / Hilbert-Mumford漸近安定性 / Caltin-Lu-Tian-Zelditch / extremal Kahle計量 / 射影kahler多様体 / Extremal metric / Zhangの臨界計量 / 漸近的ベルグマン核 / Kahler-Einstein計量 / Chow計量 |
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| Research Abstract |
(1) Related to the existence problem of extremal metrics, we studied various kinds of stabilities for manifolds For instance, we succeeded in showing that Chow-Mumford stability and Hilbert-Mumford stability are asymptotically equivalent (Chow-Mumford stability implies HiItert-Mumford stability by the work of Fogarty, while nothing was known even asymptotically about its converse).
(2) Associated to the Monge-Ampere equation for the Kahler-Einstein metric on an Einstein toric surface, we have a hyperbolic affine sphere equation with Dirichlet condition defined on a bounded convex C^<2> domain in R^<2>, and for the solution of the equation, we obtain a very explicit asymptotic expansion along the boundary.
(3) It is known that the anticanonical bundle of a toric or Kahler Einstein Fano manifold admits a Ricci-flat Kahler metric inducing a Sasaki-Einstein metric on a suitable quotient. We studied analogous examples for anticanonical bundles of Fano manifolds with Kahler-Ricci solitons.
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