Asian Journal of Mathematics

Volume 16 (2012)

Number 2

On the Yau cycle of a normal surface singularity

Pages: 279 – 298

DOI: http://dx.doi.org/10.4310/AJM.2012.v16.n2.a6

Author

Kazuhiro Konno

Abstract

The notion of the Yau sequence was introduced by Tomaru, as an attempt to extend Yau’s elliptic sequence for (weakly) elliptic singularities to normal surface singularities of higher fundamental genera. We show some fundamental properties of the sequence. Among other things, it is shown that its length gives us the arithmetic genus for singular points of fundamental genus two. Furthermore, an upper bound on the geometric genus is given for certain surface singularities of degree one. The relation between the canonical cycle and the Yau cycle is also discussed.

Keywords

Surface singularity; Yau cycle; canonical cycle

2010 Mathematics Subject Classification

14J17

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