The Gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods
arXiv:1809.02177 · doi:10.2140/gt.2020.24.2547
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.
55 pages, 7 figures, v3: added reference to arXiv:2205.00814, in which Yuto Yamamoto points out and fixes an error in our Lemma 5.6. The main results are unaffected