Blow up and integration along fibers

by baltazar   Last Updated April 25, 2018 17:20 PM

I am trying to produce an example for integration along fibers, and when I first read about this (in Arapura's book and Bott & Tu) I thought that it might be possible to apply this to the case of a blow up. Namely, say we have a quadric in $\mathbb{P^3}$ and a differential form on it. Say we blow up the quadric in one point and pull back the form to the blow-up. Then should it be possible to apply integration along fibers to get a form on the exceptional divisor?

Failing an example that involves blowing up, could you give me any example of integration along fibers? I can't seem to write down anything that works and I only have the constructions from the books, which means I must be misunderstanding something.

Thank you.

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