Tropicalization of the mirror curve near the large radius limit
Algebraic Geometry
2022-12-13 v1 Mathematical Physics
math.MP
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.
Keywords
Cite
@article{arxiv.2212.05395,
title = {Tropicalization of the mirror curve near the large radius limit},
author = {Zhaoxing Gu},
journal= {arXiv preprint arXiv:2212.05395},
year = {2022}
}