RELATIONS BETWEEN MULTIPLICITY AND DIVISOR CLASS GROUP FOR RATIONAL SURFACE SINGULARITIES
Keyword(s):
In this paper we prove that a rational surface singularity with divisor class group ℤ/(2) is a rational double point. This generalizes a result by Brieskorn: if the divisor class group of a rational singularity is trivial then it is the E8 singularity [3]. We also prove several inequalities involving the integers e, δ, mi, [Formula: see text], where [Formula: see text] is the fundamental cycle. The proof of this result uses ideas from Minkowski's theory of reduction of positive-definite quadratic forms. We also give some interesting counterexamples to some of the related questions in this context.
2014 ◽
Vol 151
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pp. 502-534
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1994 ◽
Vol 96
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pp. 97-112
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2003 ◽
Vol 46
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pp. 257-267
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2009 ◽
Vol 322
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pp. 3373-3391
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1981 ◽
pp. 146-171