L-equivalences via Symplectic and $F_4$ Grassmannians

Abstract

Using a construction of Kanemitsu from [9] and observations by Rampazzo in [19], we find examples of zero divisors in the Grothendieck ring of varieties by taking the zero loci of sections of vector bundles over symplectic and $F_4$ Grassmannians. These zero divisors yield instances of non-trivially L-equivalent Calabi-Yau varieties. This methodology is inspired by a similar process performed by Ito et al. on $G_2$ Grassmannians in [8].