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For questions related to divisors in the sense of algebraic geometry (Cartier divisors, Weil divisors and so on). For question on divisors in the number theoretic sense please use the tag divisors-multiples.

16 votes

Seeking Noetherian normal domain with vanishing Picard group but not a UFD

Here is a very simple way to find an example: If $R$ is local, then the Picard group is always trivial (because locally free = free here). So basically you want a local normal domain which is not UF …
Hailong Dao's user avatar
  • 30.6k
12 votes
Accepted

Line bundles vs. Cartier divisors on a non-integral scheme

An example is given in this note (it was credited to Kleiman).
Hailong Dao's user avatar
  • 30.6k
5 votes
Accepted

Computations of divisor class monoids

Here are a few remarks about $DC(A)$ (assuming $A$ is a complete Noetherian local domain of dimension $1$). The equivalence relation in $D(A)$ is just isomorphism as $A$-modules. So you can view $DC( …
Hailong Dao's user avatar
  • 30.6k