| 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)
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| 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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