| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
Our main work concerns construction of holomorphic curves on various types of varieties, amplifying ideas from tropical geometry. Most of the construction is based on a newly developed theory of deformations which allows us to deal with those cases which are beyond the reach of existing methods of tropical geometry. To overcome this point, we calculated the cohomology groups to which obstructions to deform degenerate curves belong, and also revealed what causes actual obstructions. As a result, we are now able to explicitly calculate obstructions in variety of cases, and then construct and classify holomorphic curves. As applications, we gave a precise relationship between periodic plane tropical curves and holomorphic curves on complex two dimensional tori, and also constructed vast number of rational curves on K3 surfaces.
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