Geodesic
Picard groups of normal surfaces
Journal of Singularities, Tome 4 (2012), pp. 154-170

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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.
DOI : 10.5427/jsing.2012.4i
Classification : 14B07, 14H10, 14H50 
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     author = {John Brevik and Scott Nollet},
     title = {Picard groups of normal surfaces},
     journal = {Journal of Singularities},
     pages = {154--170},
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     year = {2012},
     doi = {10.5427/jsing.2012.4i},
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John Brevik; Scott Nollet. Picard groups of normal surfaces. Journal of Singularities, Tome 4 (2012), pp. 154-170. doi: 10.5427/jsing.2012.4i

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