Maps between local Picard groups

TL;DR

This paper investigates the structure of local Picard groups at singularities, focusing on elements trivialized by normalization or hyperplane restriction, and improves existing results in the context of algebraic geometry.

Contribution

It introduces new insights into the behavior of local Picard groups, including an improved theorem extending previous results from SGA2.

Findings

Characterization of elements trivialized by normalization

Results on elements trivialized by hyperplane restriction

Enhanced theorem extending SGA2 results

Abstract

We study the local Picard group of singularities. We study those elements in the local Picard group that become trivial either when pulled-back to the normalization or when restricted to a hyperplane section. In the second case we improve the similar results of SGA2. Version2: Many small changes, new Theorem 4 added.