English  |  正體中文  |  简体中文  |  Items with full text/Total items : 69937/69937 (100%) Visitors : 23107346      Online Users : 709
 Scope All of NCUIR 理學院    數學研究所       --博碩士論文 Tips: please add "double quotation mark" for query phrases to get precise resultsplease goto advance search for comprehansive author search Adv. Search
 NCU Institutional Repository > 理學院 > 數學研究所 > 博碩士論文 >  Item 987654321/84279

 Please use this identifier to cite or link to this item: `http://ir.lib.ncu.edu.tw/handle/987654321/84279`

 Title: An application of Bezout′s theorem: the effective minimal intersection number of a plane curve Authors: 李詩淳;Li, Shih-Chun Contributors: 數學系 Keywords: 仿射平面曲線;交點數;Bezout定理;近似根;Embedding line;Bezout′s Theorem;intersection number;approximate roots;affine;algebraic curve Date: 2020-07-28 Issue Date: 2020-09-02 18:47:21 (UTC+8) Publisher: 國立中央大學 Abstract: 這篇碩士論文要是研究仿射平面曲線的交點數。事實上，我們將張海潮教授和王立中教授在[CW]的論述中，歸納並得出以下我們的主要定理:「如果曲線F(1,y,z)在無窮遠處只有一個place，則我們可以建構出與曲線F(1,y,z)相交的曲線G_j，使得它們在所有曲線上達到最小的正交點數。」這是應用到Bezout定理，以及在[Moh1, Moh2, Moh3, Moh4]介紹的近似根概念。此外，我們可以將Embedding Line Theorem作為一個應用並加以證明。(請參閱第八章);In this thesis, we study the intersection number of affine plane curves.Actually, we generalize the argument of Chang and Wang in [CW] to obtain our main theorem as follows:“if the curve \$F(1,y,z)\$ has only one place at infinity, then we would construct a curve G_j which intersects curve F(1,y,z) attaining the positive minimal intersection number among all curves."This is an application of Bezout′s Theorem and the approximate roots introduced by [Moh1, Moh2, Moh3, Moh4]. Besides, we can reprove the Embedding Line Theorem as an application (see section 8). Appears in Collections: [數學研究所] 博碩士論文

Files in This Item:

File Description SizeFormat
index.html0KbHTML31View/Open