| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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)
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| Outline of Final Research Achievements |
This study aims to extend the properties known for Veech surfaces of genus 2 to general genera to clarify geometric properties of Veech surfaces.The first result is the clarification of the aspect of simple closed geodesics on hyperelliptic translation surfaces of general genus. This is an extention of the properties known in the case of genus 2.The second result is that we have indicated the periodic matrices of certain hyperelliptic translation surfaces. In particular, we gave an explicit indication in the case of genus 2.The third is the classification of hyperelliptic translation surfaces of genera 3 and 4 under certain conditions. In the case of genus 3, we found that there are two types of hyperelliptic translation surfaces depending on the conditions, and we extended this to the case of genus 4.
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