On the Yau cycle of a normal surface singularity

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.