Study on effective Green conjecture

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540034
• Research Category: Grant-in-Aid for Scientific Research (C)
• 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
• 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

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.

Free Research Field

代数幾何学