The geometric genus of splice-quotient singularities

Abstract

We prove a formula for the geometric genus of splice-quotient singularities (in the sense of Neumann and Wahl). This formula enables us to compute the invariant from the resolution graph; in fact, it reduces the computation to that for splice-quotient singularities with smaller resolution graphs. We also discuss the dimension of the first cohomology groups of certain invertible sheaves on a resolution of a splice-quotient singularity.

Two examples have been added. 17 pages. To appear in Trans. Amer. Math. Soc

References in corpus (5)

• Seiberg--Witten invariants and surface singularities
• Complete intersection singularities of splice type as universal abelian covers
• Complex surface singularities with integral homology sphere links
• On the Casson Invariant Conjecture of Neumann--Wahl
• Line bundles associated with normal surface singularities

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• Geometry of splice-quotient singularities
• Némethi's division algorithm for zeta-functions of plumbed 3-manifolds
• The multiplicity of abelian covers of splice quotient singularities
• The delta invariant of curves on rational surfaces II: Poincaré series and topological aspects
• The multiplicity of generic normal surface singularities
• On the topology of surface singularities {z^n=f(x,y)}, for f irreducible
• The Seiberg-Witten invariants of negative definite plumbed 3-manifolds
• Hyperelliptic involutions on generic normal surface singularities
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• The possible values of geometric genera of normal surface singularities
• Base points of natural line bundles on relatively generic surface singularities
• Local tropicalizations of splice type surface singularities
• Brill-Noether problem on splice quotient singularities and duality of topological Poincaré series
• Analytic lattice cohomology of surface singularities
• Analytic lattice cohomology of surface singularities, II (the equivariant case)
• Class of images of Abel maps on normal surface singularities
• Invariants of relatively generic surface singularities II. Images of Abel maps
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