| DC 欄位 |
值 |
語言 |
| DC.contributor | 數學系 | zh_TW |
| DC.creator | 李詩淳 | zh_TW |
| DC.creator | Shih-Chun Li | en_US |
| dc.date.accessioned | 2020-7-28T07:39:07Z | |
| dc.date.available | 2020-7-28T07:39:07Z | |
| dc.date.issued | 2020 | |
| dc.identifier.uri | http://ir.lib.ncu.edu.tw:444/thesis/view_etd.asp?URN=107221016 | |
| dc.contributor.department | 數學系 | zh_TW |
| DC.description | 國立中央大學 | zh_TW |
| DC.description | National Central University | en_US |
| dc.description.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) | zh_TW |
| dc.description.abstract | 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). | en_US |
| DC.subject | 仿射平面曲線 | zh_TW |
| DC.subject | 交點數 | zh_TW |
| DC.subject | Bezout定理 | zh_TW |
| DC.subject | 近似根 | zh_TW |
| DC.subject | Embedding line | en_US |
| DC.subject | Bezout′s Theorem | en_US |
| DC.subject | intersection number | en_US |
| DC.subject | approximate roots | en_US |
| DC.subject | affine | en_US |
| DC.subject | algebraic curve | en_US |
| DC.title | An application of Bezout′s theorem: the effective minimal intersection number of a plane curve | en_US |
| dc.language.iso | en_US | en_US |
| DC.type | 博碩士論文 | zh_TW |
| DC.type | thesis | en_US |
| DC.publisher | National Central University | en_US |