On plane algebraic curves having only cusps as their singular points
| Project/Area Number |
22540040
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Saitama University |
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Principal Investigator |
TONO Keita 埼玉大学, 理工学研究科, 非常勤講師 (30422215)
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| Co-Investigator(Renkei-kenkyūsha) |
SAKAI Fumio 埼玉大学, 理工学研究科, 名誉教授 (40036596)
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2014: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 平面曲線 / 特異点 |
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| Outline of Final Research Achievements |
A plane algebraic curve is called cuspidal if it has only cusps as its singular points, where by a cusp I mean a locally irreducible singular point. For a cuspidal curve C on the complex projective plane let C' denote the proper transform of C via the minimal embedded resolution of the cusps. I obtained some results concerning the self-intersection number of C' for cuspidal plane curves C of genus two having only one cusp. I classified the rational cuspidal plane curves C having two cusps such that the self-intersection number of C' is equal to -1. Then I obtained an upper bound of the self-intersection number of C' for the rational cuspidal plane curves C having at least 3 cusps. Moreover, I determined the rational cuspidal plane curves C having 3 cusps such that the self-intersection number of C' is equal to the bound.
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Report
(6 results)
Research Products
(15 results)
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[Book] AFFINE ALGEBRAIC GEOMETRY2013
Author(s)
K. Masuda, H. Kojima, T. Kishimoto, I. Arzhantsev, M. Zaidenberg, M. Furushima, A. Ishida, R. V. Gurjar, M. Koras, M. Miyanishi, P. Russell, E. Kobayashi, S. Kuroda, T. Ohta, V. L. Popov, F. Sakai, Y. Takeda, R. Tanimoto, H. Yoshihara, 戸野 恵太、他
Total Pages
330
Publisher
World Scientific Publishing
Related Report
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