Pencil genus for normal surface singularities (Q873722)

In this paper the author constructs an invariant for normal complex surface singularities \((X,0)\) and for pairs \(((X,0),h)\), \(h\in \mathcal O_{X,0}\) in terms of pencils of compact complex curves. He also gives a method to construct pencils of compact complex curves from the resolution space of the surface singularity and holomorphic functions on it. The Kodaira singularities are characterized in terms of these invariants. The results are well illustrated by various examples.