Symmetry conjecture for tropical theta pairings

From papers

Let UU and VV be affine log Calabi–Yau varieties with maximal boundary, and let Sk(U)\operatorname{Sk}(U) and Sk(V)\operatorname{Sk}(V) be their skeleta. For uSk(U)u\in\operatorname{Sk}(U) and vSk(V)v\in\operatorname{Sk}(V), consider the two tropical theta pairings θvtrop(u)\theta_v^{\mathrm{trop}}(u) and θutrop(v)\theta_u^{\mathrm{trop}}(v). Symmetry conjecture. The two pairings are equal:

θvtrop(u)=θutrop(v).\theta_v^{\mathrm{trop}}(u)=\theta_u^{\mathrm{trop}}(v).

This conjecture asserts compatibility between the two mirror constructions and is used in the source to identify which theta functions are regular on a partial minimal model. The supplied text gives no evidence of resolution.

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Sources & referencesView supporting material

Primary source

Sean Keel, Logan White and Tony Yue YU, “Log Calabi-Yau mirror symmetry and non-archimedean disks”, arXiv:2411.04067 (2026).

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