Pencil genus for normal surface singularities. (English) Zbl 1140.32016

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.


32S10 Invariants of analytic local rings
32S25 Complex surface and hypersurface singularities
14J17 Singularities of surfaces or higher-dimensional varieties
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