Universal Abelian Covers of Surface Singularities
We discuss the evidence for and implications of a conjecture that the universal abelian cover of a ℚ-Gorenstein surface singularity with finite local homology (i.e., the singularity link is a ℚ-homology sphere) is a complete intersection singularity.
2000 Mathematics Subject Classification32S25, 14J17, 14B05, 57N10
Key words and phrasesGorenstein surface singularity complete intersection singularity
Unable to display preview. Download preview PDF.
- D. Eisenbud and W. D. Neumann, Three-dimensional link theory and invariants of plane curve singularities. Ann. Math. Stud. 110, Princeton. Princeton Univ. Press (1985).Google Scholar
- F. Klein, Lectures on the Icosahedron and the Solution of Equations of the Fifth Degree, Translated by George Gavin Morrice. Second andrevised ed. (Dover Publications, Inc., New York, NY, 1956).Google Scholar
- H. B. Laufer, On minimally elliptic singularities. Amer. J. Math. 99 (1977), 1257–1295.Google Scholar
- J. Milnor, On the 3-dimensional Brieskorn manifold M(p, q, r), Papers dedicated to the memory of R.H. Fox, Ann. Math. Studies 84, 175–225 (Princeton U. Press, 1975)Google Scholar
- W.D. Neumann, Abelian covers of quasihomogeneous surface singularitiesSingularities Ar- cata 1981Proc. Symp. Pure Math. 40 (Amer. Math. Soc. 1983), 233–243.Google Scholar
- W.D. Neumann, J. Wahl, Universal abelian covers of quotient-cusps. (preprint).Google Scholar
- W.D. Neumann, J. Wahl, Complete intersection singularities with integral homology sphere links (in preparation).Google Scholar