We show that every coarse moduli space, parametrizing complex special linear rank two local systems with fixed boundary traces on a surface with nonempty boundary, is log Calabi-Yau in that it has a normal projective compactification with trivial log canonical divisor. We connect this to a novel symmetry of generating series for counts of essential multicurves on the surface.

中文翻译：

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具有边界的曲面局部系统模量上的全局几何

我们表明，每个粗模空间，参数化复杂的特殊线性秩二局部系统，在具有非空边界的表面上具有固定边界迹线，是 log Calabi-Yau，因为它具有带平凡对数正则因数的正态射影紧缩。我们将其与为表面上基本多曲线的计数生成序列的新颖对称性联系起来。