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Suppose $p:P \to X$ is a projective bundle and $O(1)$ is the line bundle on $P$ restricting to $O(1)$ on each fibre. When is $p_*(O(1))$ flat on $X$?

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Hi John and welcome to MO. I'd recommend you'd edit your question so that the mathematical symbols are in math-mode. (For this see for example faq; how do I type mathematics.) –  Rami Luisto Feb 19 '13 at 16:05

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