Universal abelian covers of quotient-cusps

2001/01/30 by Walter D. Neumann, Jonathan Wahl
Mathematics · #math.AG #msc:14B05 #msc:14J17 #msc:32S25

paper · pdf

published as Math. Ann. 326 (2003), 75--93. · 16 pages

arxiv created 2001/01/30 · arxiv updated 2009/11/30

Abstract

The quotient-cusp singularities are isolated complex surface singularities that are double-covered by cusp singularities. We show that the universal abelian cover of such a singularity, branched only at the singular point, is a complete intersection cusp singularity of embedding dimension 4. This supports a general conjecture that we make about the universal abelian cover of a \Q-Gorenstein singularity.

Related

• Universal abelian covers of surface singularities
• Universal abelian covers of superisolated singularities
• Universal abelian covers of certain surface singularities
• A cusp singularity with no Galois cover by a complete intersection
• The multiplicity of abelian covers of splice quotient singularities