| Budget Amount *help |
¥17,290,000 (Direct Cost: ¥13,300,000、Indirect Cost: ¥3,990,000)
Fiscal Year 2023: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2022: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2021: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2020: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2019: ¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
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| Outline of Final Research Achievements |
The moduli spaces of stable objects on Calabi-Yau 3-folds admit d-critical structures introduced by Joyce. We introduced the notion of d-critical flips and flops between them, which are regarded as virtual birational maps. Moreover we proved that these virtual birational transformations appear as wall-crossing of stability conditions which are important in enumerative geometry. We also introduced the notion of DT categories for local surfaces which categorify Donaldson-Thomas invariants, and formulated d-critical D/K conjecture which describes the behavior under d-critical flips and flops. We also proved several properties on categorical wall-crossing of DT categories.
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