Budget Amount *help |
¥15,990,000 (Direct Cost: ¥12,300,000、Indirect Cost: ¥3,690,000)
Fiscal Year 2018: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2017: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2016: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2015: ¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
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Outline of Final Research Achievements |
We studied stability conditions on derived categories of coherent sheaves on Calabi-Yau 3-folds, and constructed moduli spaces of semistable objects. We applied this result to the study of Donaldson-Thomas invariants which count stable sheaves or curves on Calabi-Yau 3-folds. Moreover we gave mathematical definitions of Gopakumar-Vafa invariants on Calabi-Yau 3-folds and 4-folds, described conjectural relationships with Donaldson-Thomas invariants explicitly, and proved them in several cases.
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