复曲面奇点不变量

孟凡宁,袁文俊

PDF(3329 KB)
PDF(3329 KB)
广州大学学报(自然科学版) ›› 2016, Vol. 15 ›› Issue (1) : 18-26.
数学

复曲面奇点不变量

  • 孟凡宁,袁文俊*
作者信息 +

The invariants of normal complex surface singularities

  • MENG Fan-ning, YUAN Wen-jun
Author information +
History +

摘要

近几年, 作者研究了正规复曲面奇点的不变量及这些不变量之间的关系, 并得出了相应的一些结果. 文章主要综述关于Brieskorn型完全交叉曲面奇点的最优解的结构, 以及基本链、极大理想链和最小链这3个不变量之间的关系.

Abstract

In recent years, we have been studying the invariants over normal complex surface singularities and their relations, and obtained some corresponding results. In this paper, we mainly give a survey on the structure of the minimal good resolution of Brieskorn complete intersection surface singularities, and the relations among the three invariants: fundamental cycle, maximal ideal cycle and minimal cycle.

关键词

正规复曲面奇点 / Brieskorn完全交叉 / 循环商奇点 / 基本链 / 极大理想链 / 最小链

Key words

normal complex surface singularity / Brieskorn complete intersection / cyclic quotient singularities / fundamental cycles / maximal ideal cycles / minimal cycles

引用本文

导出引用
孟凡宁,袁文俊. 复曲面奇点不变量. 广州大学学报(自然科学版). 2016, 15(1): 18-26
MENG Fan-ning, YUAN Wen-jun. The invariants of normal complex surface singularities. Journal of Guangzhou University(Natural Science Edition). 2016, 15(1): 18-26

参考文献

[1] ARTIN M. On isolated rational singularities of surfaces[J]. Amer J Math, 1966, 88(1): 129-136.
[2] WAGREICH P. Elliptic singularities of surfaces[J]. Amer J Math, 1970, 92(2): 419-454.
[3] LAUFER H. On minimally elliptic singularities[J]. Amer J Math, 1977, 99(6): 1257-1295.
[4] KARRAS U. On pencils of curves and deformations of minimally elliptic singularities[J]. Math Ann, 1980, 247(1): 43-65.
[5] STEVENS J. Elliptic surface singularities and smoothings of curves[J]. Math Ann, 1984, 267(2): 239-249.
[6] YAU S S T. On maximally elliptic singularities[J]. Trans Amer Math Soc, 1980, 257(2): 269-329.
[7] NMETHI A. “Weakly” elliptic Gorenstein singularities of surfaces[J]. Invent Math, 1999, 137(1): 145-167.
[8] NMETHI A. Invariants of normal surface singularities[J]. Real Complex Singul (Contemp Math, 354), Amer Math Soc, Provid, RI, 2004, 161-208.
[9] TOMARU T. On Gorenstein surface singularities with fundamental genus pf≥2 which satisfy some minimality conditions[J]. Pacif J Math, 1995, 170(1): 271-295.
[10]TOMARU T. On Kodaira singularities defined by zn=f(x,y)[J]. Math Zeitschrift, 2001, 236(1): 133-149.
[11]TOMARU T. Complex surface singularities and degenerations of compact complex curves[J]. Demonst Math, 2010, 43(2): 339-359.
[12]KONNO K, NAGASHIMA D. Maximal ideal cycles over normal surface singularities of Brieskorn type[J]. Osaka J Math, 2012, 49(1): 225-245.
[13]MENG F N, OKUMA T. The maximal ideal cycles over complete intersection surface singularities of Brieskorn type[J]. Kyushu J Math, 2014, 68(1): 121-137.
[14]STEVENS J. Kulikov singularities[D]. Holland: Universiteit Leiden, 1985.
[15]NEUMANN W D. A calculus for plumbing applied to the topology of complex surface singularities and degenerating complex curves[J]. Trans Amer Math Soc, 1981, 268(2): 299-344.
[16]LAUFER H B. Normal two-dimensional singularities[M]. Ann Math Studies, No.71, Princeton: Princeton University Press, 1971.
[17]BARTH W P, Hulek K, PETERS C A M, et al. Compact complex surfaces[M]. 2nd ed. Ergebnisse der Math und ihrer Gren, 3, Folge, a series of Modern Surveys in Math, 4, Berlin: Springer-Verlag, 2004.
[18]NMETHI A. Five lectures on normal surface singularities[J]. Bolyai Soc Math Stud, 1999, 8: 269-351.
[19]HIRZEBRUCH F. Uber vierdimensionale Riemannsche Flachen mehrdeutiger analytischer Funktionen von zwei komplexen Veranderlichen[J]. Math Ann, 1953, 126: 1-22.
[20]TOMARU T. C*-equivariant degenerations of curves and normal surface singularities with C*-action[J]. J Math Soc Japan, 2013, 65(3): 829-885.
[21]LAUFER H B. On rational singularities[J]. Amer J Math, 1972, 94: 597-608.
[22]OKUMA T. Plurigenra of surface singularities[M]. Huntington: New York, Nova Science Publishers, 2000.
[23]TOMARU T. A formula of the fundamental genus for hypersurface singularities of Brieskorn type[J]. Ann Rep Coll Med Care Tech Gunma Univ, 1996, 17: 145-150.

基金

国家自然科学基金资助项目 (10771220); 教育部留学回国人员科研启动基金资助项目; 广东省自然科学基金资助项目(2015A030313346, S2012010010121)
PDF(3329 KB)

124

Accesses

0

Citation

Detail

段落导航
相关文章

/