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Results tagged with divisors
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user 1784
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.
10
votes
Line bundles vs. Cartier divisors on a non-integral scheme
Cartier divisors) to $H^1( O^*)$ (i.e. line bundles) is surjective. … So the example would have to be a scheme with embedded primes with a tricky nonconstant $K^*$ (the sheaf of nonzero divisors). I've seen it but can't remember right now. …
- 13.1k
28
votes
Accepted
Contracting divisors to a point
For a smooth $Y$, a necessary condition for contractibility is that the conormal line bundle $N_{Y,X}^*$ is ample. It is also sufficient for contracting to an algebraic space. The reference is Algebra …
- 13.1k