Picard groups of normal surfaces
John Brevik and Scott Nollet
Journal of Singularities
volume 4 (2012), 154-170
Received: 25 July 2012. Received in revised form: 14 October 2012.
Add a reference to this article to your citeulike library.
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 contained in 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 from 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.
Mathematical Subject Classification:
14B07, 14H10, 14H50
Author(s) information:
John Brevik | Scott Nollet |
California State University at Long Beach | Texas Christian University |
Department of Mathematics and Statistics | Department of Mathematics |
Long Beach, CA 90840 | Fort Worth, TX 76129 |
email: jbrevik@csulb.edu | email: s.nollet@tcu.edu |