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I'm trying to understand the proof at the top of page 3 of

http://math.stanford.edu/~vakil/02-245/sclass6A.pdf

http://math.stanford.edu/~vakil/02-245/sclass6B.pdf

Why can $D$ and D' be moved in their linear equivalence class in such a way that they intersect transversely AND such that their intersection lies in $U$? Intuitively this makes sense, of course, but what are the formal arguments?

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    Thank you for answering. However I don't see how we can get a transversal intersection...2012-03-14

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