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

Abouzaid, Mohammed¹ ; Ganatra, Sheel² ; Iritani, Hiroshi³ ; Sheridan, Nick⁴

¹ Department of Mathematics, Columbia University, New York, NY, United States
² Department of Mathematics, University of Southern California, Los Angeles, CA, United States
³ Department of Mathematics, Kyoto University, Kyoto, Japan
⁴ School of Mathematics, University of Edinburgh, Edinburgh, United Kingdom

Geometry & topology, Tome 24 (2020) no. 5, pp. 2547-2602.

Résumé

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.

Détail

DOI : 10.2140/gt.2020.24.2547

Classification : 53D37, 11G42, 14J33, 14T05, 32G20
Keywords: mirror symmetry, SYZ conjecture, periods, tropical geometry, Riemann zeta values, Gamma class, Batyrev mirror

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