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作者(中文):張有鄰
作者(外文):Chang, Yu-Lin
論文名稱(中文):Waldschmidt常數的Demailly猜想:一個改良的充分條件與Nagata/Iarrobino猜想下的證明
論文名稱(外文):Demailly Conjecture on Waldschmidt constant in P^n: an improved sufficient condition and a proof assuming Nagata/Iarrobino Conjecture
指導教授(中文):卓士堯
指導教授(外文):Jow, Shin-Yao
口試委員(中文):陳俊成
吳思曄
口試委員(外文):Chen, Jiun-Cheng
Wu, Siye
學位類別:碩士
校院名稱:國立清華大學
系所名稱:數學系
學號:103021505
出版年(民國):107
畢業學年度:106
語文別:英文
論文頁數:18
中文關鍵詞:代數幾何
外文關鍵詞:algebraic geometry
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在這論文中我們討論了一些關於 Waldschmidt constant 的結果。其中一個主要的結果是Nagata/Iarrobino猜想與Demailly猜想之間的關係:在 Pn上隨意選取的點夠大時,在前者的猜想假設下後者成立。另外我們也把參考文獻[14]裡的主要定理做一個改良。
In this note, we discuss some results about Waldschmidt constant. One of the main results presents a relation between Nagata/Iarrobino Conjecture and Demailly Conjecture: the former implies the latter, for large enough number of general points in Pn, n ≥ 2. In addition, we also present an improvement of the main theorem in [14].
1 Introduction---------------------------------------------------1
2 Preliminary----------------------------------------------------2
3 Some containment problems between symbolic and ordinary powers-6
4 A Lower bound of Waldschmidt constant related to the number of
general points-------------------------------------------------8
5 Proof of Theorem 1.2------------------------------------------12
6 Proof of Theorem 1.3------------------------------------------16
Reference-------------------------------------------------------18
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[2] G. V. Chudnovsky, Singular points on complex hypersurfaces and multidimensional
Schwarz Lemma, Seminaire de Theorie des Nombres, Paris 1979–80, Seminaire Delange-Pisot-Poitou, Progress in Math vol. 12, M-J Bertin, editor, Birkhauser, Boston-Basel-Stutgart 1981.
[3] J.-P. Demailly, Formules de Jensen en plusieurs variables et applications arithmétiques, Bull. Soc. Math. France 110. (1982), 75–102.
[4] M. Dumnicki, T. Szemberg, H. Tutaj-Gasinska, Counterexamples to the I(3) ⊂ I2 containment, J. Algebra 393 . (2013) 24–29.
[5] M. Dumnicki, H. Tutaj-Gasi´nska, A containment result in Pn and the Chudnovsky Conjecture, Proc. Amer. Math. Soc. 145. (2017), 3689–3694.
[6] H. Esnault, E. Viehweg, Sur une minoration du degré d’hypersurfaces s’annulant en certains points, Math. Ann. 263 . (1983), no. 1, 75–86.
[7] L. Evain, On the postulation of sd fat points in Pd, J. Algebra 285 . (2005) 516–530.
[8] L. Fouli, P. Mantero, Y. Xie, Chudnovsky’s conjecture for very general points in P Nk, J. Algebra 498. (2018) 211–227.
[9] B. Harbourne, C. Huneke, Are symbolic powers highly evolved?, J. Ramanujan Math. Soc. (2011), arXiv:1103.5809.
[10] A. Hirschowitz, La méthode d’Horace pour l’interpolation à plusieurs variables, Manuscripta Math. 50. (1985) , 337–388.
[11] M. Hochster, C. Huneke, Comparison of symbolic and ordinary powers of ideals, Invent. Math. 147. (2002), no. 2, 349-369.(arXiv:math/0211174)
[12] M. Hochster, C. Huneke, Fine behavior of symbolic powers of ideals, Illinois J. Math. 51. (2007) 171–183.
[13] T. Iarrobino, Inverse system of a symbolic power III: thin algebras and fat points, Compositio Math. 108. (1997) 319–356.
[14] G. Malara, T. Szemberg, J. Szpond, On a conjecture of Demailly and new bounds on Waldschmidt constants in PN , J. Number Theory 189 (2018) 211-219.
[15] J.-C. Moreau, Lemmes de Schwarz en plusieurs variables et applications arithmétiques, Séminaire Pierre Lelong-Henri Skoda (Analyse). Années 1978/79 (French), in: Lecture Notes in Math., vol.822, Springer, Berlin–New York. (1980) 174–190.
[16] M. Nagata, On the 14-th problem of Hilbert, Amer. J. Math. 81. (1959) 766-772.
[17] H. Skoda, Estimations L2 pour l’opérateur ˜∂ et applications arithmétiques, Séminaire P. Lelong (Analyse), 1975/76, Lecture Notes Math. 578, Springer-Verlag. (1977) 314-323.
[18] M. Waldschmidt, Propriétés arithmétiques de fonctions de plusieurs variables II,
Séminaire P. Lelong (Analyse), 1975–76, Lecture Notes Math. 578, Springer-Verlag. (1977) 108–135.
[19] M. Waldschmidt, Nombres transcendants et groupes algébriques, Astérisque 69/70, Socéte Mathématiqué de France. (1979).
 
 
 
 
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