| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| Outline of Final Research Achievements |
We show that a surgery corresponding to the chain relations in the mapping class groups of surfaces can decrease the Kodaira dimensions of total spaces of Lefschetz fibrations. Moreover, by analyzing examples of Lefschetz fibrations appearing in the proof of this result, we construct new counterexamples of the Stipsicz conjecture on fiber-sum decomposability and existence of sections of Lefschetz fibrations.
We completely classify genus-1 holomorphic Lefschetz pencils and obtain vanishing cycles of the Lefschetz pencils in the classification list.
Baykur and Saeki gave an algorithm to obtain trisection mappings from (broken) Lefschetz fibrations. We give an algorithm to determine tirsection diagrams corresponding to trisection mappings obtained by Baykur-Saeki's algorithm from vanishing cycles of original (broken) Lefschetz fibrations.
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