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研究生： 王賜聖
Sz-Sheng Wang
論文名稱： 多層扭變多重典型形式的擴張
Extensions of multiply twisted pluri-canonical form
指導教授： 王金龍
Chin-Lung Wang
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
畢業學年度： 97
語文別： 英文
論文頁數： 29
外文關鍵詞： pluricanonical forms, invariance of plurigenera, Ohsawa-Takegoshi
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    • 在本篇文章中，我們主要的工具是Ohsawa-Takegoshi定理，這是由蕭蔭堂老師所敘述並証明的版本[7]。透過Păun在[5]証明多重虧格不變性定理所使用的技巧，我們証明了在光滑射影族的纖維上，附帶著某種可積性的多重典型形式，可以被擴張到整個光滑射影族。

    Using Siu''s version of the Ohsawa-Takegoshi theorem and the techniques in proving the invariance of plurigenera developed by Siu [7] and Păun [5], we show that for a smooth projective family pluri-canonical forms with integrable pseudo-effective twi-
    sted coefficients may be lifted from the central fiber to the ambient family.

    1 Introduction...........................................1 2 Preliminaries..........................................2 3 A moA modification of Siu and Păun''s induction.........7 3.1 A choice of the ample line bundle..................8 3.2 Inductive procedure................................9 4 Proof of Theorem 1.1..................................14 4.1 From L^2-estimates to supremum norm estimates.....14 4.2 Siu''s construction of the metric and conclusion of the proof ...17 References…………..21

    [1] B. Claudon;Invariance of plurigenera for multiples of the twisted canonical bundle
    [2] J.-P. Demailly; Analytic approach of the minimal model program and of the abundance conjectures
    [3] J.-P. Deamailly, L. Ein and R. Lazarsfeld; A subadditivity property of multiplier ideals
    [4] P. Lelong and L. Gruman; Entire functions of several complex variables
    [5] M. Păun; Siu''s invariance of plurigenera: a one-tower proof
    [6] Y.-T. Siu; Invarince of plurigenera
    [7] Y.-T. Siu; Extension of twisted pluricanonical sections with plurisubharmonic weight and invariance of semipositively twisted plurigenera for manifolds not necessarily of general type

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