Journal of the Mathematical Society of Japan

Another proof of the end curve theorem for normal surface singularities

Tomohiro OKUMA

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Neumann and Wahl introduced the notion of splice-quotient singularities, which is a broad generalization of quasihomogeneous singularities with rational homology sphere links, and proved the End Curve Theorem that characterizes splice-quotient singularities. The purpose of this paper is to give another proof of the End Curve Theorem. We use combinatorics of “monomial cycles” and some basic ring theory, whereas they applied their theory of numerical semigroups.

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J. Math. Soc. Japan Volume 62, Number 1 (2010), 1-11.

First available in Project Euclid: 5 February 2010

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Mathematical Reviews number (MathSciNet)

Primary: 32S25: Surface and hypersurface singularities [See also 14J17]
Secondary: 14B05: Singularities [See also 14E15, 14H20, 14J17, 32Sxx, 58Kxx] 14J17: Singularities [See also 14B05, 14E15]

surface singularity splice-quotient singularity rational homology sphere splice type singularity universal abelian cover


OKUMA, Tomohiro. Another proof of the end curve theorem for normal surface singularities. Journal of the Mathematical Society of Japan 62 (2010), no. 1, 1--11. doi:10.2969/jmsj/06210001.

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