In arXiv:1809.03737 and arXiv:1809.03744 the authors investigated invariants of generic analytic structures on surface singularities and determined some of them like the geometric genus of generic surface singularities or $h^1$ of generic line bundles with a given Chern class on an arbitrary surface singularity. There are however other invariants of generic surface singularities, like multiplicity or embedded dimension we wish to compute in following manuscripts in the case of generic singularities... (read more)
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