The geometric genus of splice-quotient singularities

2006/10/16 by Tomohiro Okuma, Okuma, Tomohiro
Mathematics · #14B05 (Secondary) #32S25 (Primary) #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0610464

openalex publication_date 2006/10/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Line bundles associated with normal surface singularities

Related

• The cohomology of line bundles of splice-quotient singularities
• The multiplicity of abelian covers of splice quotient singularities
• On the topology of surface singularities zⁿ=f(x,y), for f irreducible
• Geometry of splice-quotient singularities
• Splice diagrams and splice-quotient surface singularities