A counterexample to the birational Torelli problem for Calabi-Yau threefolds

@article{Ottem2018ACT,
title={A counterexample to the birational Torelli problem for Calabi-Yau threefolds},
author={J. C. Ottem and J{\o}rgen Vold Rennemo},
journal={J. Lond. Math. Soc.},
year={2018},
volume={97},
pages={427-440}
}

The Grassmannian Gr(2, 5) is embedded in P via the Plücker embedding. The intersection of two general PGL(10)-translates of Gr(2, 5) 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 , deformation equivalent to X. Applying results of Kuznetsov and Jiang–Leung–Xie shows that X and Y are derived equivalent, which by a result of Addington implies that their third cohomology groups are isomorphic as polarised Hodge structures… CONTINUE READING