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arXiv · 2212.05395

Tropicalization of the mirror curve near the large radius limit

Zhaoxing Gu
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Abstract

The mirror of a toric orbifold is an affine curve called the mirror curve. In this paper, firstly, we recall the basic tools in tropical geometry and give a definition of the mirror curve. Then we calculate the tropical spine of the mirror curve for a smooth toric Calabi-Yau 3-fold near the large radius limit. Finally, we recall a special kind of real algebraic curves called the cyclic-M curve and show that under some special choices of parameters near the large radius limit, the mirror curve is a cyclic-M curve. Applying Mikhalkin's result of cyclic-M curves, we show that the mirror curve is glued from tubes and pairs of pants.

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Zhaoxing Gu. 2022-12-11. Tropicalization of the mirror curve near the large radius limit. https://arxiv.org/abs/2212.05395

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