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Results tagged with divisors
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user 2083
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.
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( …
- 30.6k
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 …
- 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).
- 30.6k