Algebraic Geometry Seminar

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Intersections of two Grassmannians in P^9

Speaker: Alexander Perry, Columbia University

Location: Warren Weaver Hall 317

Date: Tuesday, October 10, 2017, 3:30 p.m.

Synopsis:

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.