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 $G_2$.

arXiv comment5 pages, reference added, minor changes

References in corpus (2)

• The Fano variety of lines and rationality problem for a cubic hypersurface
• Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians

Cited by in corpus (9)

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• Complete intersection Calabi--Yau manifolds with respect to homogeneous vector bundles on Grassmannians
• Intersections of two Grassmannians in ${\mathbf{P}}^9$
• Motives and the Pfaffian-Grassmannian equivalence
• Birational geometry and derived categories
• An example of birationally inequivalent projective symplectic varieties which are D-equivalent and L-equivalent
• Automorphisms of positive entropy on some hyperKahler manifolds via derived automorphisms of K3 surfaces
• Hilbert schemes of two points on K3 surfaces and certain rational cubic fourfolds
• $G_2$-Grassmannians and derived equivalences