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    政大機構典藏 > 理學院 > 應用數學系 > 學位論文 >  Item 140.119/55095
    Please use this identifier to cite or link to this item: https://nccur.lib.nccu.edu.tw/handle/140.119/55095

    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
    Li, Wei De
    Keywords: K穩定性
    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.
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    [9] M. Kapranov. Amoebas over non-archimedean fields. Preprint. 2000.
    [10] Z. Lu. On the Futaki invariants of complete intersections. Duke Mathematical Journal. 100(2): 359–372, 1999.
    [11] Z. Lu. K energy and K stability on hypersurfaces. Communications in Analysis and Geometry. 12(3): 599-628, 2004.
    [12] T. Mabuchi. K energy maps integrating Futaki invariants. Tohoku Mathematical Journal. 38: 245–257, 1986.
    [13] Y. Matsushima. Sur la structure du group d`homeomorphismes analytiques d`une certaine varietie Kahleriennes. Nagoya Mathematical Journal. 11: 145–150, 1957.
    [14] D. H. Phong and J. Sturm. Algebraic estimates, stability of local zeta functions, and uniform estimates for distribution functions. Annals of Mathematics II. 152(1): 277–329, 2000.
    [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.
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    [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
    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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