Taiwanese Journal of Mathematics

The Minimal Cycles over Brieskorn Complete Intersection Surface Singularities

Fanning Meng, Wenjun Yuan, and Zhigang Wang

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In this paper, we study a complete intersection surface singularity of Brieskorn type and provide a condition for the coincidence of the fundamental cycle and the minimal cycle on the minimal resolution space.

Article information

Taiwanese J. Math., Volume 20, Number 2 (2016), 277-286.

First available in Project Euclid: 1 July 2017

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Zentralblatt MATH identifier

Primary: 14J17: Singularities [See also 14B05, 14E15]
Secondary: 32S25: Surface and hypersurface singularities [See also 14J17]

normal surface singularities cyclic quotient singularities Brieskorn complete intersections fundamental cycle minimal cycle


Meng, Fanning; Yuan, Wenjun; Wang, Zhigang. The Minimal Cycles over Brieskorn Complete Intersection Surface Singularities. Taiwanese J. Math. 20 (2016), no. 2, 277--286. doi:10.11650/tjm.20.2016.6434. https://projecteuclid.org/euclid.twjm/1498874441

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  • F. Hirzebruch, Über vierdimensionale Riemannsche Flächen mehrdeutiger analytischer Funktionen von zwei komplexen Veränderlichen, Math. Ann. 126 (1953), 1–22.
  • K. Konno and D. Nagashima, Maximal ideal cycles over normal surface singularities of Brieskorn type, Osaka J. Math, 49 (2012), no. 1, 225–245.
  • H. B. Laufer, On rational singularities, Amer. J. Math. 94 (1972), 597–608.
  • ––––, On minimally elliptic singularities, Amer. J. Math. 99 (1977), no. 6, 1257–1295.
  • F.-N. Meng and T. Okuma, The maximal ideal cycles over complete intersection surface singularities of Brieskorn type, Kyushu J. Math. 68 (2014), no. 1, 121–137.
  • W. D. Neumann, Abelian covers of quasihomogeneous surface singularities, Singularities, Part 2 (Arcata, Calif., 1981), 233–243, Proc. Sympos. Pure Math., 40 Amer. Math. Soc., Providence, RI, 1983.
  • J. Stevens, Kulikov singularities, Thesis, 1985.
  • T. Tomaru, On Gorenstein surface singularities with fundamental genus $p_f \geq 2$ which satisfy some minimality conditions, Pacific J. Math. 170 (1995), no. 1, 271–295.
  • P. Wagreich, Elliptic singularities of surfaces, Amer. J. Math. 92 (1970), no. 2, 419–454.
  • S. S. T. Yau, On maximally elliptic singularities, Trans. Amer. Math. Soc. 257 (1980), no. 2, 269–329.