Geometry of splice-quotient singularities

Abstract

We obtain a new important basic result on splice-quotient singularities in an elegant combinatorial-geometric way: every level of the divisorial filtration of the ring of functions is generated by monomials of the defining coordinate functions. The elegant way is the language of of line bundles based on Okuma's description of the function ring of the universal abelian cover. As an easy application, we obtain a new proof of the End Curve Theorem of Neumann and Wahl.

arXiv comment17 pages, 2 figures, bad line breakings with dvips because hyperlinked texts are not broken

References in corpus (6)

• 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
• Line bundles associated with normal surface singularities
• Surgery formula for Seiberg--Witten invariants of negative definite plumbed 3-manifolds
• The cohomology of line bundles of splice-quotient singularities

Cited by in corpus (1)

• The multiplicity of abelian covers of splice quotient singularities