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研究生: 鄭治平
Chih-Ping Cheng
論文名稱:
Very ampleness of toric 3-folds
指導教授: 林惠雯
Hui-Wen Lin
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: 24
中文關鍵詞: 環面簇
外文關鍵詞: ample divisor, toric variety
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  • 西元2004年,張秀卿於其碩士論文中給出在三維的環面簇裡,一些特別的、其一倍後會是 very ample 的 ample divisor。根據此問題,本篇論文給出一個必要條件及一些一般結果。


    In 2004,Hsiu-Ching Chang gave some special ample divisors in toric 3-folds which are very ample. Our main result is to give a necessary condition for this problem and to find a general result for this problem.

    1.Introduction‧‧‧‧‧‧‧‧‧‧‧‧1 2. Review of Toric Geometry‧‧‧‧‧‧2 2.1. Basic notations‧‧‧‧‧‧‧‧‧‧2 2.2. Divisors‧‧‧‧‧‧‧‧‧‧‧‧‧2 2.3. Related theorems‧‧‧‧‧‧‧‧‧3 3. Main Results‧‧‧‧‧‧‧‧‧‧‧‧4 References‧‧‧‧‧‧‧‧‧‧‧‧‧‧21

    1. G. Ewald and U. Wessels; On the ampleness of invertible sheaves in complete projective toric varietiesResults Math. 19(1991), 275-278.
    2. W. Fulton; Introduction to toric varieties, Princeton University Press, Princeton, NJ, 1993.
    3. V. Danilov; The geometry of toric varieties, Russian Math. Surveys 33 (1978), 97-154.
    4. G. Kempf, F. Knudsen, D. Mumford, and B. Saint-Donat; Toroidal embeddings I, Lectures Notes in Math., 339, Springer-Verlag, Berlin, 1973.
    5. T. Oda; Convex bodies and algebraic geometry, Springer-Verlag, New York, 1988.
    6. R. Hartshorne; Ample subvarieties of Algebraic Varieties, Springer-Verlag, LNM 156.
    7. Cheng-Fu Chen; A remark on very-ampleness in Toric geometry, Master Thesis, National Central University, 2003.
    8. Hsiu-Ching Chang; Special ample divisors in toric 3-folds, Master Thesis, National Central University, 2004.
    9. Yueng-Zhi Cai; An effective construction to resolve singularities on toric varieties (general case), Master Thesis, National Central University, 2004.
    10. Chung-Kuei Li; Existence problems about crepant resolutions of diagonal hypersurfaces, Master Thesis, National Central University, 2008.

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