Abstract
We consider a germ of a two-dimensional complex singularity \((X,x_0)\), irreducible at \(x_0\) and \(F\) the exceptional divisor of a desingularization. We prove that if there exists a normal isolated singularity \((Z,z_0)\) with simply connected link and a surjective holomorphic map \(f:(Z,z_0)\rightarrow (X,x_0)\) then all irreducible components of \(F\) are rational, and if all irreducible components of \(F\) are rational then there exists a surjective holomorphic map \(f:(\mathbb {C}^2,0)\rightarrow (X,x_0)\).
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Acknowledgments
We would like to thank the referee for very useful remarks. Both authors were supported by CNCS Grant PN-II-ID-PCE-2011-3-0269.
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Communicated by Alexander Isaev.
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Colţoiu, M., Joiţa, C. On the Parameterization of Germs of Two-Dimensional Singularities. J Geom Anal 25, 2427–2435 (2015). https://doi.org/10.1007/s12220-014-9520-3
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DOI: https://doi.org/10.1007/s12220-014-9520-3