The class of the affine line is a zero divisor in the Grothendieck ring: via K3 surfaces of degree 12

Atsushi Ito, Makoto Miura, Shinnosuke Okawa, Kazushi Ueda

Published 2016-12-27Version 1

We show that general K3 surfaces of degree 12 come in non-isomorphic Fourier-Mukai pairs $(X, Y)$ satisfying $[\mathbb{A}^3] \cdot ([X]-[Y]) = 0$ in the Grothendieck ring of varieties.