On the motive of Kapustka-Rampazzo's Calabi-Yau threefolds

TL;DR

This paper proves that certain pairs of Calabi-Yau threefolds, previously known to be derived and L-equivalent but not birational, also share isomorphic Chow motives, deepening understanding of their geometric relationships.

Contribution

It establishes that these Calabi-Yau threefold pairs have isomorphic Chow motives, completing the picture of their equivalences beyond derived and L-equivalence.

Findings

X and Y have isomorphic Chow motives

X and Y are L-equivalent and derived equivalent

X and Y are not birational

Abstract

Kapustka and Rampazzo have exhibited pairs of Calabi-Yau threefolds $X$ and $Y$ that are L-equivalent and derived equivalent, without being birational. We complete the picture by showing that $X$ and $Y$ have isomorphic Chow motives.