The class of the affine line is a zero divisor in the Grothendieck ring: via $G_2$-Grassmannians

Abstract

Motivated by [Bor] and [Mar], we show the equality $\left([X]-[Y]\right)\cdot [{\mathbb{A}}^1]=0$ in the Grothendieck ring of varieties, where $(X,Y)$ is a pair of Calabi-Yau 3-folds cut out from the pair of Grassmannians of type $G_2$.

5 pages, reference added, minor changes

References in corpus (1)

• The Fano variety of lines and rationality problem for a cubic hypersurface

Cited by in corpus (3)

• Birational geometry and derived categories
• Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces
• $G_2$-Grassmannians and derived equivalences