An application of Bezout′s theorem: the effective minimal intersection number of a plane curve

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:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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