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edited May 15 at 12:58

I want to prove Castelnuovo's contraction theorem by Mori's contraction theorem.

How to show $(-1)$ curve on surface is extremal ray.

Question. How can one show that a $(-1)$ curve on a smooth surface is an extremal ray?

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asked May 15 at 11:07

Contraction of $(-1)$ curve and extremal ray

I want to prove Castelnuovo's contraction theorem by Mori's contraction theorem.

How to show $(-1)$ curve on surface is extremal ray.