Study on effective Green conjecture
Project/Area Number |
24540034
|
Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | The University of Tokyo |
Principal Investigator |
MIYAOKA Yoichi 東京大学, 数理(科)学研究科(研究院), 教授 (50101077)
|
Project Period (FY) |
2012-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
|
Keywords | ヒッグズ層 / スペクトル分解 / 制限定理 / テンソル積定理 / Bogomolov 不等式 / 半安定 Higgs 束 / 積定理 / Miyaoka-Yau 不等式 / ヒッグズ束 / 半安定性 / Mehta-Ramanathan 型定理 / エフェクティブな Green-Lang 予想 / 代数曲面 / 標準次数 / 尖点曲線 / オービフォールド / B-M-Y 不等式 |
Outline of Final Research Achievements |
We studied subvarieties and vector bundles on algebraic varieties. The main result obtained by our project is the construction of purely algebraic theory of Higgs bundles. We proved among others the following basic results: 1) general spectral decompositions of Higgs bundles; 2) the restriction theorem and the product theorem, which assert that semistability of Higgs bundles is preserved by restriction to general hypersurfaces and by tensor products; and 3) the Bogomolov inequality for characteristic classes of semistable Higgs bundles. Thanks to the above results, the theory of Higgs bundles is as useful in algebraic geometry as is the theory of ordinary vector bundles.
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Report
(4 results)
Research Products
(5 results)