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Jun 17, 2010 at 10:41 comment added GS Thanks! Due to my shocking level of ignorance I had not looked at Huybrechts' book. You actually undersell the conjecture there: it asserts that if there exists a birational correspondence between (smooth, projective over alg. closed field of char. 0---seem to be standing assumptions) varieties that matches up canonical classes then the 2 varieties in question are derived equivalent (though the equivalence need not be induced by the given birational correspondence). Since I'm also interested in the question about flops, I hope you don't mind if I don't accept this helpful answer!
Jun 15, 2010 at 19:29 history answered achatz CC BY-SA 2.5