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Jan 2, 2013 at 7:46 comment added rita The fact that $S$ is minimal is irrelevant here, and Riemann-Roch is not used, either. The point, as explained in Donu's comment above, is that the intersection number is independent of the fiber.
Jan 1, 2013 at 23:56 vote accept Matt Grimes
Jan 1, 2013 at 23:56 comment added Matt Grimes Ah! So then knowing that the self-intersection number of a fibre is $0$ and Riemann-Roch tell us that $K.F=K.G$ for a general fibre $G$? Thank you for the response.
Jan 1, 2013 at 21:27 history answered Jonathan CC BY-SA 3.0