On the motive of intersections of two Grassmannians in ${\mathbb{P}}^9$

Abstract

Using intersections of two Grassmannians in ${\mathbb{P}}^9$, Ottem-Rennemo and Borisov-C\u{a}ld\u{a}raru-Perry have exhibited pairs of Calabi-Yau threefolds $X$ and $Y$ that are deformation equivalent, L-equivalent and derived equivalent, but not birational. To complete the picture, we show that $X$ and $Y$ have isomorphic Chow motives.