Invariants of relatively generic structures on normal surface singularities

Abstract

In the present article we work out a relative setup of generic structures on surface singularities. We fix an analytic type on a subgraph of a rational homology sphere resolution graph $\mathcal{T}$ and we choose a relatively generic normal surface singularity $\tX$ with resolution graph $\mathcal{T}$. We provide formulae for the geometric genus and the analytical Poincaré series of $\tX$. We determine the base point structure of natural line bundles on $\tX$ and give a lower bound on the multiplicity of $\tX$ which is expected to be sharp. We prove similar results about cohomology numbers of relatively generic line bundles on every singularity with rational homology sphere link.

References in corpus (5)

• Seiberg--Witten invariants and surface singularities
• Complete intersection singularities of splice type as universal abelian covers
• The geometric genus of splice-quotient singularities
• On the Casson Invariant Conjecture of Neumann--Wahl
• Durfee's conjecture on the signature of smoothings of surface singularities

Cited by in corpus (8)

• Cohomology of natural line bundles on generic normal surface singularities
• Hyperelliptic involutions on generic normal surface singularities
• The multiplicity of generic normal surface singularities
• Normal reduction numbers of normal surface singularities
• Invariants of relatively generic surface singularities II. Images of Abel maps
• The possible values of geometric genera of normal surface singularities
• Class of images of Abel maps on normal surface singularities
• Base points of natural line bundles on relatively generic surface singularities