发表机构
Tata Institute of Fundamental Research-Centre for Applicable Mathematics（塔塔基础研究所应用数学中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究Fock逆谱变换在热带极限下的行为，证明其与热带化可交换，并推导出Fay三割线恒等式的热带版本。
AI 中文摘要
二聚体谱变换为簇可积系统提供了代数几何作用-角坐标。Fock给出了其逆变换的显式公式。我们在热带极限下研究Fock的逆映射，其中Harnack谱曲线退化为结点曲线。我们确定了Fock公式中出现的经典对象的首阶渐近行为，并表明它们由其热带对应物支配。这就在热带谱数据上产生了一个热带逆谱变换。我们证明Fock的逆谱变换与热带化可交换，并推导出Fay三割线恒等式的热带版本。
英文摘要
The dimer spectral transform gives algebro-geometric action-angle coordinates for cluster integrable systems. Fock gave an explicit formula for its inverse. We study Fock's inverse map in the tropical limit where Harnack spectral curves degenerate to nodal curves. We determine the leading order asymptotics of the classical objects appearing in Fock's formula and show that they are governed by their tropical counterparts. This yields a tropical inverse spectral transform on tropical spectral data. We show that Fock's inverse spectral transform commutes with tropicalization, and also derive a tropical version of Fay's trisecant identity.
Comments47 pages, 10 figures
