, Volume 326, Issue 1, pp 75-93

Universal abelian covers of quotient-cusps

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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.

Received: 3 February 2001 / Revised version: 8 March 2002 / Published online: 10 February 2003
Mathematics Subject Classification (2000): 14B05, 14J17, 32S25
This research was supported by grants from the Australian Research Council and the NSF (first author) and the the NSA (second author).