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The
Gamma and Strominger–Yau–Zaslow conjectures: a tropical
approach to periods
Mohammed Abouzaid, Sheel Ganatra, Hiroshi Iritani and Nick Sheridan |
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Geometry & Topology 24 (2020) 2547–2602
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Abstract |
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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. |
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Keywords
mirror symmetry, SYZ conjecture, periods, tropical
geometry, Riemann zeta values, Gamma class, Batyrev mirror
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Mathematical Subject Classification 2010
Primary: 53D37
Secondary: 11G42, 14J33, 14T05, 32G20
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References |
Publication
Received: 26 February 2019
Revised: 28 October 2019
Accepted: 26 November 2019
Published: 29 December 2020
Proposed: Richard P Thomas
Seconded: Paul Seidel, Dan Abramovich
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Authors |
| Mohammed Abouzaid | |
| Department of Mathematics Columbia University New York, NY United States |
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| Sheel Ganatra | |
| Department of Mathematics University of Southern California Los Angeles, CA United States |
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| Hiroshi Iritani | |
| Department of Mathematics Kyoto University Kyoto Japan |
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| Nick Sheridan | |
| School of Mathematics University of Edinburgh Edinburgh United Kingdom |
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