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arXiv · 2512.07762

Skein-valued mirror curves for toric CY3 strips

Mingyuan Hu·Vivek Shende
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Abstract

For a smooth semi-projective toric Calabi-Yau 3-fold containing no compact surface, we show the count of all-genus holomorphic curves with boundary on a single Aganagic-Vafa brane is annihilated by a skein-valued quantization of the mirror curve, and that this determines the count. We give explicit expressions for the equation and its solution.

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Mingyuan Hu, Vivek Shende. 2025-12-08. Skein-valued mirror curves for toric CY3 strips. https://arxiv.org/abs/2512.07762

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