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| 研究生： |
李威德 Li, Wei De |
|---|---|
| 論文名稱： |
K 穩定性與熱帶幾何之研究 On K Stability and Tropical Geometry |
| 指導教授： |
蔡炎龍
Tsai, Yen Lung |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2012 |
| 畢業學年度： | 100 |
| 語文別： | 英文 |
| 論文頁數： | 53 |
| 中文關鍵詞： | K穩定性 、熱帶幾何 、法諾超平面 |
| 外文關鍵詞： | K stability, tropical geometry, Fano hypersurface |
| 相關次數： | 點閱：161 下載：58 |
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在這篇論文中，我們從K energy的角度探討緊緻法諾超平面上的K穩定性。首先，我們給K energy一個較明確的型式，接著再透過分析的手法求解其導函數。後續，我們引進熱帶幾何的結構來重新分析主要的結果，最後給一些法諾超平面的實例，驗證我們所得到的公式。
In this thesis, we analyze K stability on compact Fano hypersurfaces from K energy. We first represent the K energy into an explicitly formula. Then we compute the derivative by using some analytic techniques. Furthermore, we introduce some structures of tropical geometry to analyze the main result. Finally, we give some examples of compact Fano hypersurface to test and verify the formula we get.
謝辭 .......................... i
Abstract .......................... iii
中文摘要 .......................... iv
Content .......................... v
1 Introduction .......................... 1
2 Tropical Geometry .......................... 8
3 An explicit formula for the K energy .......................... 16
4 The limit of the derivative of the K energy .......................... 27
5 Some Examples .......................... 43
References .......................... 52
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