| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
Based on the iterations of remainder and round-down maps of multi-fractions, we defined a new type of multidimensional continued fraction as a certain non-commutative polynomial. Moreover, we extended the relation among the Hirzebruch-Jung resolution of 2-dimensional cyclic quotient singularities and the classical continued fractions to the relation among the Fujiki-Oka resolution of higher-dimensional cyclic quotient singularities and our multidimensional continued fractions. With respect to the classification problem of the fiber germs of non-hyperelliptic fibrations of genus 3 via their Horikawa indices, our calculation was finished by using the classification of automorphisms of stable curves of genus 3, an extension of Eichler's trace formula and the expression of the local signature defect via the Dedekind sum. Although the paper about it is not yet completed, and we are making efforts on it.
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