The fundamental divisor of normal double points of surfaces

David Dixon

Vol. 80 (1979), No. 1, 105–115

DOI: 10.2140/pjm.1979.80.105

Abstract

Let W be a surface with a normal singular point w. Consider the minimal resolution of that singularity, π;W′→ W. Let π⁻¹(w) = Y = Y ₁⋯Y _d, where the Y _i are distinct irreducible curves on W′. We are interested in two divisors on W′ both 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