Invariants of relatively generic structures on normal surface singularities

János Nagy

Published 2019-10-08Version 1

In \cite{NNA1} and \cite{NNA2} the authors investigated invariants of generic analytic structures on surface singularities and determined many 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 like the multiplicity of generic surface singularities or class of the images of Abel maps we wish to compute in following manuscripts. In the present article we work out a relative setup of generic structures on surface singularities, where we fix a given analytic type or line bundle on a smaller subgraph or more generally on a smaller cycle and we choose a relatively generic line bundle or analytic type on the large cycle and we wish to compute it's invariants, like geometric genus or $h^1$. The formulas which give the answers to these questions are quite intresting on their own, however the real power of these results, that they give possibility for inductive proofs of problems regarding generic surface singularities.