Hello, I'm interested in the case when all varieties are projective threefolds over the complex numbers.


Start with a flopping contraction $f:Y \rightarrow X$, with corresponding flop $f^+: Y^+ \rightarrow X$. It has been [proved](http://www.tombridgeland.staff.shef.ac.uk/papers/flop.pdf) that there then exists an equivalence $\Phi : D^b(Y^+) \rightarrow D^b(Y)$.


Is there a way to understand this (or any other) equivalence explicitly? 


I've heard there is a way to find an equivalence by considering a common resolution of $Y$ and $Y^+$ and then using derived pullback and pushforward, is it true?


I am mostly interested in what happens to sheaves on $Y^+$ supported on the exceptional locus.


Thanks.



Is there a nice way to characterise the derived equivalence induced by a flop?
As always, it depends on what you think "explicitly" means. It's a Fourier-Mukai transform; see, for example, [Van den Bergh and Hille's expository article](http://alpha.uhasselt.be/Research/Algebra/Publications/hille.pdf). It can also be explained in terms of so-called non-commutative crepant resolutions, [see Van den Bergh](http://alpha.uhasselt.be/Research/Algebra/Publications/flops.ps).


