The geometry of higher Weierstrass points and moduli spaces of plane algebraic curves
Project/Area Number |
23540041
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Saitama University |
Principal Investigator |
SAKAI Fumio 埼玉大学, 理工学研究科, 教授 (40036596)
|
Research Collaborator |
KAWASAKI Masumi 海城高等学校, 教諭
WANGYU Nan 瀋陽師範大学, 講師
FARAHAT Mohamed Al-Azhar University, 講師
|
Project Period (FY) |
2011-04-28 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
|
Budget Amount *help |
¥5,070,000 (Direct Cost: ¥3,900,000、Indirect Cost: ¥1,170,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2011: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
|
Keywords | 代数幾何 / 平面代数曲線 / 特異点 / ワイエルシュトラス点 / ゴナリティ / モジュライ |
Outline of Final Research Achievements |
We studied 3-Weierstrass points on genus two curves with extra involutions. We obtained new criterion for the gonality of singular plane curves. In particular, in case the maximal multiplicity of the singular points is equal to three, we obtained the almost optimal criterion. We introduced a new invariant V defined by the multiplicities of singular points. We also considered the lower bound of the gonality. We classified hyperelliptic curves among cyclic coverings of the projective line. We published papers on these topics.
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Report
(5 results)
Research Products
(14 results)