2014 Fiscal Year Final Research Report
Study on effective Green conjecture
Project/Area Number 
24540034

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Multiyear 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) 
20120401 – 20150331

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
