Fundamental Cycles Of Surface Singularities Defined By A Cubic Equation

The fundamental cycle is an important invariant of a singularity, which was introduced by M.Artin in his paper [1] in 1966. In the theories of singularities and the classification of algebraic surfaces, it is a fundamental problem to compute this cycle explicitly from the resolution of a singularity. A. Calabri and R. Ferraro [11] obtained a formula to compute the fundamental cycle of a double surface singularity from the well-known canonical resolution. We will give in this paper the computation formula of the fundamental cycles of surface singularities defined by cubic equations based on the canonical resolution.