 Self-intersection after blowing up points on a smooth curve

ID: self-intersection-after-blowing-up-points-on-a-smooth-curve

r

distinct smooth points of a smooth curve

C

C^{'}

isomorphic to

C

with

(C^{'})^{2} = C^{2} - r .

Choosing

r > C^{2}

turns a curve of positive self-intersection into one of negative self-intersection without changing its abstract isomorphism type.

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