English  |  正體中文  |  简体中文  |  Post-Print筆數 : 27 |  Items with full text/Total items : 109874/140825 (78%)
Visitors : 45912656      Online Users : 983
RC Version 6.0 © Powered By DSPACE, MIT. Enhanced by NTU Library IR team.
Scope Tips:
  • please add "double quotation mark" for query phrases to get precise results
  • please goto advance search for comprehansive author search
  • Adv. Search
    HomeLoginUploadHelpAboutAdminister Goto mobile version
    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
    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.
    [2] D. Burns and P. De Bartolomeis. Stability of vector bundles amd extremal metrics. Inventions Mathematicae. 92(2):403–407, 1988.
    [3] W. Y. Ding and G. Tian. Kähler-Einstein metrics and the generalized Futaki invariant. Inventions Mathematicae. 110: 315–335, 1992.
    [4] M. Einsiedler, M. Kapranov and D. Lind. Non-Archimedean amoebas and tropical varieties. ArXiv preprint:math.AG/0408311, 2004.
    [5] S. K. Donaldson. Scalar curvature and stability of toric varieties. Journal of Differential Geometry. 62(2): 289–349, 2002.
    [6] A. Futaki. An obstruction to the existence of Einstein- Kähler metrics. Inventions Mathematicae. 73: 437–443, 1983.
    [7] A. Gathmann. Tropical algebraic geometry. Jahresbericht der Deutschen Mathematiker-Vereinigung. 108(1): 3–32, 2006.
    [8] Y. J. Hong. Gauge-fixing constant scalar curvature equations on ruled manifolds and the Futaki invariants. Journal of Differential Geometry. 60(3): 389–453, 2002.
    [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.
    [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

    Files in This Item:

    File SizeFormat
    004101.pdf1029KbAdobe PDF2960View/Open


    All items in 政大典藏 are protected by copyright, with all rights reserved.


    社群 sharing

    著作權政策宣告 Copyright Announcement
    1.本網站之數位內容為國立政治大學所收錄之機構典藏,無償提供學術研究與公眾教育等公益性使用,惟仍請適度,合理使用本網站之內容,以尊重著作權人之權益。商業上之利用,則請先取得著作權人之授權。
    The digital content of this website is part of National Chengchi University Institutional Repository. It provides free access to academic research and public education for non-commercial use. Please utilize it in a proper and reasonable manner and respect the rights of copyright owners. For commercial use, please obtain authorization from the copyright owner in advance.

    2.本網站之製作,已盡力防止侵害著作權人之權益,如仍發現本網站之數位內容有侵害著作權人權益情事者,請權利人通知本網站維護人員(nccur@nccu.edu.tw),維護人員將立即採取移除該數位著作等補救措施。
    NCCU Institutional Repository is made to protect the interests of copyright owners. If you believe that any material on the website infringes copyright, please contact our staff(nccur@nccu.edu.tw). We will remove the work from the repository and investigate your claim.
    DSpace Software Copyright © 2002-2004  MIT &  Hewlett-Packard  /   Enhanced by   NTU Library IR team Copyright ©   - Feedback