| Budget Amount *help |
¥17,940,000 (Direct Cost: ¥13,800,000、Indirect Cost: ¥4,140,000)
Fiscal Year 2015: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2014: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2013: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2012: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2011: ¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
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| Outline of Final Research Achievements |
We studied the derived categories of coherent sheaves on algebraic varieties from many aspects. We obtained (1) a counterexample to birational Torelli problem, (2) full exceptional collections on toric varieties by Frobenius morphisms, (3) a classification of exceptional sheaves on a Hirzebruch surface and (4) a description of the autoequivalences groups on minimal elliptic surfaces. We applied our study on Fourier--Mukai partners on elliptic surfaces to obtain (1). The result (2) is a generalization of the McKay correspondence. The study in (4) should be generalized in the cases of any algebraic surfaces.
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