Motivic Zeta Functions of the Quartic and its Mirror Dual

TL;DR

This paper computes the motivic zeta function for a quartic K3 surface and its mirror dual using Bultot's formula, confirming a key mirror symmetry prediction at an integral level.

Contribution

It provides an explicit calculation of motivic zeta functions for a K3 surface and its mirror, validating theoretical mirror symmetry predictions.

Findings

Motivic zeta functions explicitly computed for quartic K3 and mirror dual.

Verification of monodromy and Lefschetz operator correspondence at an integral level.

Supports mirror symmetry conjectures through concrete examples.

Abstract

We use a formula of Bultot to compute the motivic zeta function for the toric degeneration of the quartic K3 and its Gross-Siebert mirror dual degeneration. We check for this explicit example that the identification of the logarithm of the monodromy and the mirror dual Lefschetz operator works at an integral level.