On Gorenstein surface singularities with fundamental genusp_f≧ 2 which satisfy some minimality conditions

Kulikov singularities

“…Furthermore the resolution graph of x a + y b + t c−d is a subgraph of the resolution graph of x a + y b + t c . The Proposition was proved by Tomaru [17] using an explicit description of the resolution of the singularity. As to this resolution, we note that there are r chains of c 1 − 1 (−2)-curves from the characteristic cycle to the components of X.…”

“…The above result extends with the same proof to the case of Brieskorn complete intersections. A proof in the style of [17] was given by Meng, Yuan and Wang [9].…”

“…The generalisation of Laufer's minimally elliptic cycle [7] is the characteristic cycle, introduced by Karras for Kodaira singularities [5] and in [16] in general. Tomaru studied for which Brieskorn singularities the characteristic cycle is equal to the fundamental cycle [17] .…”

“…In this paper I actually take this as definition (see Definition 2.1), being the shortest, but it is the construction using a family of curves which gives a good understanding of the singularity. As illustration I treat the results of Némethi and Okuma [12] and of Tomaru [17] from this point of view.…”

On the Yau cycle of a normal surface singularity

“…In this paper, we study surface singularities by considering decompositions of various cycles on π −1 (o). One of the main objects is the Yau sequence introduced by Tomaru [9], which formally generalizes S.S.T. Yau's elliptic sequence [11] to singularities of bigger fundamental genera.…”