| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2022: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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)
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| Outline of Final Research Achievements |
In this project, we studied the problem of the geography of fibrations of algebraic curves on a non-singular projective algebraic curve with specific structures which is the question of what values of the relative Euler-Poincare characteristic, the self-intersection number of the relative canonical divisor and the genus of a fiber can take. We mainly considered fibrations given by triple coverings of projective line bundles, and proved inequalities among these invariants that depending on the type of branch loci. In particular, we show that the lower bounds on the slope and the Euler-Poincare characteristic differ from each other depending on whether the genus of a fiber is congruent to 2 modulo 3 or not. Furthermore, we specifically gave triple coverings of projective line bundles and proved the existence of fibrations of algebraic curves.
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