PICARD GROUPS OF NORMAL SURFACES

We study the fixed singularities imposed on members of a linear system of surfaces in P-C(3), by its base locus Z. For a 1-dimensional subscheme Z subset of P-3 with finitely many points p(i), of embedding dimension three and d >> 0, we determine the nature of the singularities p(i) is an element of S for general S is an element of vertical bar H-0 (P-3, I-z(d))vertical bar and give a method to compute the kernel of the restriction map CIS -> CIOs, pi. One tool developed is an algorithm to identify the type of an A n singularity via its local equation. We illustrate the method for representative Z and use Noether-Lefschetz theory to compute Pic S.