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| Title: | K 穩定性與熱帶幾何之研究
On K Stability and Tropical Geometry |
| Authors: | 李威德
Li, Wei De |
| Contributors: | 蔡炎龍
Tsai, Yen Lung
李威德
Li, Wei De |
| Keywords: | K穩定性
熱帶幾何
法諾超平面
K stability
tropical geometry
Fano hypersurface |
| Date: | 2011 |
| Issue Date: | 2012-10-30 16:27:29 (UTC+8) |
| Abstract: | 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. |
| Reference: | [1] T. Aubin. Equations du type de Monge-Ampére sur les variétés Kähleriennes compactes. C. R. Acad. Sci. Paris. 283: 119-121, 1976.
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[12] T. Mabuchi. K energy maps integrating Futaki invariants. Tohoku Mathematical Journal. 38: 245–257, 1986.
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[15] J. Ross and R. Thomas. A study of the Hilbert-Mumford criterion for the stability of projective varieties, Journal of Differential Geometry. 16(2): 201–255, 2007.
[16] G. Tian. The K- energy on hypersurfaces and stability. Communications in Analysis and Geometry. 2(2): 239–265, 1994.
[17] G. Tian. Kähler-Einstein metrics with positive scalar curvature. Inventions Mathematicae. 137: 1–37, 1997.
[18] S. T. Yau. On the Ricci curvature of a compact Kähler manifold and the complex Monge- Ampére equation, I. Communications on Pure and Applied Mathematics. 31: 339–441, 1978. |
| Description: | 碩士
國立政治大學
應用數學研究所
99751004
100 |
| Source URI: | http://thesis.lib.nccu.edu.tw/record/#G0997510041 |
| Data Type: | thesis |
| Appears in Collections: | [應用數學系] 學位論文
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