| Project/Area Number |
17K14172
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Algebra
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| Research Institution | Nara Medical University |
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Principal Investigator |
Kawaguchi Ryo 奈良県立医科大学, 医学部, 助教 (10573694)
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| Project Period (FY) |
2017-04-01 – 2020-03-31
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| Project Status |
Completed (Fiscal Year 2019)
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| Budget Amount *help |
¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2019: ¥390,000 (Direct Cost: ¥300,000、Indirect Cost: ¥90,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
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| Keywords | 代数幾何学 / 偏極多様体 / 断面幾何種数 / トーリック多様体 / Weierstrass半群 |
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| Outline of Final Research Achievements |
It is well known that tovic varieties are closely related with convex polytopes. In this study, we make use of this property to investigate various problems of algebraic geometry and algebraic combinatorics. As a result, we found the equivalence of the upper bound for the sectional genus of a polarized variety and the lower bound for the volume of a convex polytope. We also conducted a study of Weierstrass semigroups. A Weierstrass semigroup with prime degree satisfies a numerical condition called the MP condition if it is cyclic, but the converse is not valid in general. In this issue, we have proved the converse is true for a semigroup of a pointed curve on a toric surface.
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| Academic Significance and Societal Importance of the Research Achievements |
図形(代数多様体)を方程式の解集合として捉える代数幾何学において, トーリック多様体は多面体の幾何学と深いつながりを持った特殊な多様体群であり, 重要な不変量の多くを対応する多面体の形や体積, 格子点の数といった情報から読み取ることができる. 不変量の一つである断面幾何種数には上限の公式があり, 多面体の体積については下限の公式が知られているが, 本研究ではこれらの公式が同値(つまり種数が上限に等しいことと対応する多面体の体積が下限に等しいことが同値)であることを発見した. 他にも, Weierstrass半群の巡回性に関する研究を行った.
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