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 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.