The Gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods

TL;DR

This paper introduces a tropical geometry-based method to analyze period asymptotics, revealing natural appearances of zeta values and providing new insights into the Gamma class and Strominger-Yau-Zaslow conjecture, with applications to mirror symmetry.

Contribution

It presents a novel tropical approach to compute period asymptotics, connecting the Gamma class with the Strominger-Yau-Zaslow conjecture and offering a new proof of the Gamma Conjecture for mirror Calabi-Yau hypersurfaces.

Findings

Zeta values emerge as error terms in tropicalization.

A new proof of the Gamma Conjecture for Batyrev pairs.

Insights into the Gamma class from tropical geometry.

Abstract

We propose a new method to compute asymptotics of periods using tropical geometry, in which the Riemann zeta values appear naturally as error terms in tropicalization. Our method suggests how the Gamma class should arise from the Strominger-Yau-Zaslow conjecture. We use it to give a new proof of (a version of) the Gamma Conjecture for Batyrev pairs of mirror Calabi-Yau hypersurfaces.