L-equivalences via Symplectic and $F_4$ Grassmannians

TL;DR

This paper constructs examples of zero divisors in the Grothendieck ring of varieties using sections over symplectic and F4 Grassmannians, leading to non-trivially L-equivalent Calabi-Yau varieties, inspired by previous work on G2 Grassmannians.

Contribution

It introduces a new method to produce zero divisors in the Grothendieck ring via vector bundle sections over specific Grassmannians, expanding the understanding of L-equivalence among Calabi-Yau varieties.

Findings

Identified zero divisors in the Grothendieck ring from symplectic and F4 Grassmannians.

Constructed non-trivially L-equivalent Calabi-Yau pairs.

Extended techniques previously applied to G2 Grassmannians to other types.

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].