List of known Fourier Mukai partners? I'm familiar with some examples of pairs of derived equivalent varieties, for example an abelian variety and its dual, a K3 surface and certain moduli schemes on it, or the Pfaffian-Grassmannian derived equivalence.
However, when I looked for other known examples, I could only find papers constructing single examples of Fourier-Mukai partners, and no comprehensive survey.
Can anyone provide references where I can find out more about known Fourier-Mukai partners, giving me a broad overview?
 A: There are actually several known Fourier Mukai partners. 


*

*Standard flop/Atiyah flop. See Chapter 11 of Fourier-Mukai Transforms in Algebraic Geometry by Huybrechts. 

*Mukai flops (Chapter 11 of Fourier-Mukai Transforms in Algebraic Geometry by Huybrechts), stratified Mukai flops https://arxiv.org/abs/1111.0688 and Grassmannian flops https://arxiv.org/abs/1206.0219.

*Abouf flops https://arxiv.org/abs/1706.04417 and Ueda flops https://arxiv.org/abs/1812.10688. 

*Any birational but non-isomorphic projective Calabi-Yau 3-folds. See http://www.tom-bridgeland.staff.shef.ac.uk/publications/pub6.pdf

*Examples from Homological Projective Duality (HPD), e.g. intersection of two $G(2,5)$ and the intersection of the dual Grassmannian (https://arxiv.org/abs/1707.00534), the intersection of two spinor varieties of $Spin(10)$ and the intersection of their duals(https://arxiv.org/abs/1709.07736). Both of these pairs are non-birtional Calabi-Yau's. The general theorem about the derived equivalences and the kernel functors can refer to https://arxiv.org/abs/1804.00144 and https://arxiv.org/abs/1704.01050

*Pair of Calabi-Yau 3 folds in $G_2$ Grassmannian. https://arxiv.org/pdf/1611.08386.pdf It should be noted that these CY3 are non-birational.


I think there are many examples of FM partners from birational geometry, moduli spaces, and HPD theory.
