| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Outline of Final Research Achievements |
Using the fact where the Cohen-Macaulay cone is pointed at the origin indicates that there is a finite number of numerical equivalence classes of maximal Cohen-Macaulay modules of rank r for each natural number r. If the given ring is a 3-dimensional hypersurface isolated singularity, it can be proved that, for rank 1 modules, the numerical equivalence class and the linear equivalence class coincide by using the argument of theta pairing. From this, it was found that, in the case of a 3-dimensional hypersurface isolated singularity, there is only finite number of rank 1 maximal Cohen-Macaulay modules up to isomorphism.
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