研究生: |
黃鐘響 CHUNG-HSIANG HUANG |
---|---|
論文名稱: |
HILBERT-KUNZ 函數在 C_3-QUARTICS CURVES 中有4重根. THE HILBERT-KUNZ FUNCTION OF C_3-QUARTICS CURVES HAVING A ZERO OF ORDER 4. |
指導教授: |
洪有情
Hung, Yu-Ching |
學位類別: |
碩士 Master |
系所名稱: |
數學系 Department of Mathematics |
畢業學年度: | 87 |
語文別: | 中文 |
論文頁數: | 17 |
中文關鍵詞: | HILBERT-KUNZ |
英文關鍵詞: | HILBERT-KUNZ |
論文種類: | 學術論文 |
相關次數: | 點閱:306 下載:0 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
令 f=p_1(x,z)y^3+p_4(x,z) 是一個NON-DEGENERATE C_3-QUARTICS ,且p_4有4重根,則 f 的HILBERT-KUNZ 函數是(1)13/4*^p^(2n) 若p^(2n)跟4同餘
(2)13/4*p^(2n)-9/4 若不是的話
Let f=p_1(x,z)y^3+p_4(x,z) be a non-degenerate C_3 guartic, and p_4 have order 4 zero. Then the Hilbert-Kunz function of the hypersurface f is
(1)13/4*^p^(2n) if p^(2n)=4*k
(2)13/4*p^(2n)-9/4 otherwise
1.Buchweitz-Chen, Hilbert-Kunz functions of cubic curves and surfaces. J. Algebra 197(1997) 246-267.
2.L. Chiang and Y.C. hung, On Hilbert-Kunz function and representation ring. Bull. Inst. Math. Acad. Sinica 26 (1998).
3.L. Chiang, Hilbert-Kunz functions, Doctoral Thesis, National Taiwan Normal University, 1996.
4.L. Chiang and Y.C. Hung, On Hilbert-Kunz functions of some hypersurfaces. J. Algebra. 199 (1998) 499-527.
5.A. Conca, Hilbert-Kunz function of monomial ideals and binomial hypersurfaces. Manuscripta Math. 90 (1996) 287-300.
6.M. Contessa, On Hilbert-Kunz function and Koszul homology. J. Algebra. 175(1995)757-766.
7.D. Cox, J.Little and D.O'Shea, "Ideal, Varieties, and Algorithms," Springer-Verlag, New York/Berlin/Heidelburg, 1992.
8. C. Han, The Hilbert-Kunz function of a diagonal hypersurface, Doctoral Thesis, Brandeis University, 1992.
9. C. Han and P. Monsky, Some surprising Hilbert-Kunz functions, Math, Z. 214 (1993), 119-135.
10. E. Kunz, On Noetherian rings of characteristic p, Amer. J. Math. 98 (1976), 999-1013.
11.P. Monsky, The Hilbert-Kunz function, Math. Ann. 263 (1983), 43-49.
12. P. Monsky, The Variation of Hilbert-Kunz in families: point- quartics. J. Algebra. 197 (1997).
13. P. Monsky, The variation of Hilbert-Kunz in families: -quartics, p=2.
14. H. Regnath and G. Seibert, A generalization of a result of Monsky on the Hilbert-Kunz function.
15. G. Seibert, The Hilbert-Kunz function of rings of finite Cohen-Macaulay type. Arch. Math. 69 (1997) 286-296.