The gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods. (English) Zbl 1467.14097
Summary: 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.
MSC:
| 14J33 | Mirror symmetry (algebro-geometric aspects) |
| 14T20 | Geometric aspects of tropical varieties |
| 53D37 | Symplectic aspects of mirror symmetry, homological mirror symmetry, and Fukaya category |
| 11G42 | Arithmetic mirror symmetry |
| 32G20 | Period matrices, variation of Hodge structure; degenerations |
Keywords:
mirror symmetry; SYZ conjecture; periods; tropical geometry; Riemann zeta values; gamma class; Batyrev mirrorReferences:
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