Abstract
Given a normal affine surface V defined over \({\mathbb{C}}\), we look for algebraic and topological conditions on V which imply that V is smooth or has at most rational singularities. The surfaces under consideration are algebraic quotients \({\mathbb{C}^n/G}\) with an algebraic group action of G and topologically contractible surfaces. Theorem 3.6 can be considered as a global version of the well-known result of Mumford giving a smoothness criterion for a germ of a normal surface in terms of the local fundamental group.
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Research supported by the RIP-program at Mathematisches Forschungsinstitut Oberwolfach.
M. Koras is supported by Polish Grant MNiSW. M. Miyanishi is supported by Grant-in-Aid for Scientific Research (C), JSPS. P. Russell is supported by NSERC, Canada.
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Gurjar, R.V., Koras, M., Miyanishi, M. et al. Affine normal surfaces with simply-connected smooth locus. Math. Ann. 353, 127–144 (2012). https://doi.org/10.1007/s00208-011-0675-y
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DOI: https://doi.org/10.1007/s00208-011-0675-y