Class of the affine line is a zero divisor in the Grothendieck ring

TL;DR

This paper demonstrates that the class of the affine line acts as a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers, using the Pfaffian-Grassmannian double mirror correspondence.

Contribution

It introduces a novel proof that the affine line's class is a zero divisor in the Grothendieck ring, leveraging mirror symmetry techniques.

Findings

The class of the affine line is a zero divisor in the Grothendieck ring.

Mirror symmetry provides a new approach to understanding algebraic variety classes.

The result impacts the structure of the Grothendieck ring and its algebraic properties.

Abstract

We show that the class of the affine line is a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers. The argument is based on the Pfaffian-Grassmannian double mirror correspondence.