The Gamma and Strominger–Yau–Zaslow conjectures: a tropical approach to periods
| Autor: | Sheel Ganatra, Nick Sheridan, Hiroshi Iritani, Mohammed Abouzaid |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Class (set theory)
Pure mathematics 11G42 14J33 mirror symmetry Batyrev mirror 32G20 01 natural sciences Gamma class 53D37 symbols.namesake Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry SYZ conjecture 14T05 0103 physical sciences Tropical geometry FOS: Mathematics 0101 mathematics Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics Conjecture 010308 nuclear & particles physics 010102 general mathematics Riemann zeta function Riemann zeta values Mathematics - Symplectic Geometry periods tropical geometry symbols Symplectic Geometry (math.SG) Geometry and Topology Mathematics::Differential Geometry Mirror symmetry |
| Zdroj: | Geom. Topol. 24, no. 5 (2020), 2547-2602 ABOUZAID, MOHAMMED, Ganatra, S, IRITANI, HIROSHI & Sheridan, N 2020, ' The Gamma and Strominger-Yau-Zaslow conjectures: a tropical approach to periods ', Geometry and Topology, vol. 24, no. 5, pp. 2547–2602 . https://doi.org/10.2140/gt.2020.24.2547 |
| DOI: | 10.2140/gt.2020.24.2547 |
| Popis: | 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. Comment: 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 |
| Databáze: | OpenAIRE |
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