Vol. 80, No. 1, 1979

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The fundamental divisor of normal double points of surfaces

David Dixon

Vol. 80 (1979), No. 1, 105–115
Abstract

Let W be a surface with a normal singular point w. Consider the minimal resolution of that singularity, π;W′→ W. Let π1(w) = Y = Y 1Y d, where the Y i are distinct irreducible curves on W. We are interested in two divisors on Wboth of which have support on Y . These divisors are Z, the fundamental divisor, and M, the divisor of the maximal ideal. In general Z M. In this thesis we show that if w is a double point singularity which satisfies certain conditions, then Z = M.

Mathematical Subject Classification 2000
Primary: 14B05
Secondary: 14C20, 14J17
Milestones
Received: 12 December 1977
Published: 1 January 1979
Authors
David Dixon