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

TL;DR

This paper investigates the relationships between certain Calabi-Yau threefolds derived from intersections of Grassmannians in projective space, establishing their isomorphic Chow motives and deepening understanding of their geometric and motivic properties.

Contribution

It proves that the Calabi-Yau threefolds constructed from Grassmannian intersections have isomorphic Chow motives, extending previous results on their equivalences.

Findings

X and Y are deformation equivalent, L-equivalent, and derived equivalent.

X and Y have isomorphic Chow motives.

The work completes the understanding of the motivic relationship between these threefolds.

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.