The birational Torelli problem for Calabi-Yau 3-folds

The intersection of two general PGL(10)-translates of the Grassmannian Gr(2,5)
in P9 is a Calabi-Yau 3-fold X, and the intersection of the projective duals of
the two translates is another Calabi-Yau 3-fold Y. We show that X and Y provide
counterexamples to a certain ”birational” Torelli problem for Calabi-Yau 3-folds,
namely, they are deformation equivalent, derived equivalent, and have isomorphic
Hodge structures, yet they are not birational.
This is joint work with Jørgen Vold Rennemo.