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I have to do a lesson (1 h.) about a very basic introduction to intersection theory. In order to do this I'd like to find a way in order to examplain the concept of rational equivalence giving a lot of examples. Could you suggest me examples of interesting rational equivalences?

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The simplest example of rational equivalence is the linear equivalence of divisors. This is already quite a rich situation. Perhaps you'd want to talk about that a bit. Then, perhaps you could talk about equivalence of correspondences on curves.

However, the interesting thing is usually not to show that two cycles are linearly equivalent, but to show that they are not!

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