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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.
11
votes
Contracting divisors to a point
In the case of smooth surfaces, this is already a tough question :
If E is a rational curve, then E can be contracted to a point in a smooth variety if the self-intersection $E\cdotp E=-1$ (thm of C …