Picard Groups of Normal Surfaces
Algebraic Geometry
2016-01-25 v1
Abstract
We study the fixed singularities imposed on members of a linear system of surfaces in P^3_C by its base locus Z. For a 1-dimensional subscheme Z \subset P^3 with finitely many points p_i of embedding dimension three and d >> 0, we determine the nature of the singularities p_i \in S for general S in |H^0 (P^3, I_Z (d))| and give a method to compute the kernel of the restriction map Cl S \to Cl O_{S,p_i}. 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.
Cite
@article{arxiv.1208.0269,
title = {Picard Groups of Normal Surfaces},
author = {John Brevik and Scott Nollet},
journal= {arXiv preprint arXiv:1208.0269},
year = {2016}
}