The class of the affine line is a zero divisor in the Grothendieck ring: Via 𝐺₂-Grassmannians

Abstract

Motivated by [J. Algebraic Geom. 27 (2018), pp. 203–209] and [C. R. Math. Acad. Sci. Paris 354 (2016), pp. 936–939], we show the equality ( [ X ] − [ Y ] ) ⋅ [ A 1 ] = 0 \left ( [ X ] - [ Y ] \right ) \cdot [ \mathbb {A} ^{ 1 } ] = 0 in the Grothendieck ring of varieties, where ( X , Y ) ( X, Y ) is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type G 2 G _{ 2 } .