Algebraic Geometry Seminar
I will discuss the intersection of two copies of Gr(2,5) embedded in P^9, and the intersection of the two projectively dual Grassmannians in the dual projective space. These intersections are deformation equivalent Calabi-Yau threefolds. I will explain why they are derived equivalent but generically not birational, and use this to obtain a counterexample to the birational Torelli problem for Calabi-Yau threefolds, as well as new examples of zero divisors in the Grothendieck ring of varieties. This is joint work with Lev Borisov and Andrei Caldararu.