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Jul 24, 2015 at 13:18 comment added David E Speyer Thank you for explaining this! I read through that proof pretty carefully in order to teach it a few years ago, and didn't come up with nearly as good a way to summarize it. (See math.lsa.umich.edu/~speyer/632Old/apr-12.pdf if you are curious.) One thing I do find helpful is to point out the stronger result $H^q(X, L \otimes \Omega^p)=0$, for $p+q>n$. That makes the $(p,q)$ symmetry much more clear.
Jul 24, 2015 at 7:31 history answered user61522 CC BY-SA 3.0